Reciprocals of Leftins

The following is a list of the reciprocals of all the integers from 1 to 30 in various number bases.

Observations on the reciprocals.

base 2

00000000000000000000000000000001
00000000000000000000000000000001
---
00000000000000000000000000000010
 0000000000000000000000000000000.1
---
00000000000000000000000000000011
10101010101010101010101010101011
---
00000000000000000000000000000100
  000000000000000000000000000000.01
---
00000000000000000000000000000101
11001100110011001100110011001101
---
00000000000000000000000000000110
 1010101010101010101010101010101.1
---
00000000000000000000000000000111
10110110110110110110110110110111
---
00000000000000000000000000001000
   00000000000000000000000000000.001
---
00000000000000000000000000001001
00111000111000111000111000111001
---
00000000000000000000000000001010
 1100110011001100110011001100110.1
---
00000000000000000000000000001011
10111010001011101000101110100011
---
00000000000000000000000000001100
  101010101010101010101010101010.11
---
00000000000000000000000000001101
11000100111011000100111011000101
---
00000000000000000000000000001110
 1011011011011011011011011011011.1
---
00000000000000000000000000001111
11101110111011101110111011101111
---
00000000000000000000000000010000
    0000000000000000000000000000.0001
---
00000000000000000000000000010001
11110000111100001111000011110001
---
00000000000000000000000000010010
 0011100011100011100011100011100.1
---
00000000000000000000000000010011
00101000011010111100101000011011
---
00000000000000000000000000010100
  110011001100110011001100110011.01
---
00000000000000000000000000010101
00111100111100111100111100111101
---
00000000000000000000000000010110
 1011101000101110100010111010001.1
---
00000000000000000000000000010111
11101001101111010011011110100111
---
00000000000000000000000000011000
   10101010101010101010101010101.011
---
00000000000000000000000000011001
11000010100011110101110000101001
---
00000000000000000000000000011010
 1100010011101100010011101100010.1
---
00000000000000000000000000011011
01101000010010111101101000010011
---
00000000000000000000000000011100
  101101101101101101101101101101.11
---
00000000000000000000000000011101
01001111011100101100001000110101
---
00000000000000000000000000011110
 1110111011101110111011101110111.1

base 3

00000000000000000000000000000001
00000000000000000000000000000001
---
00000000000000000000000000000002
11111111111111111111111111111112
---
00000000000000000000000000000010
 0000000000000000000000000000000.1
---
00000000000000000000000000000011
20202020202020202020202020202021
---
00000000000000000000000000000012
21012101210121012101210121012102
---
00000000000000000000000000000020
 1111111111111111111111111111111.2
---
00000000000000000000000000000021
10212010212010212010212010212011
---
00000000000000000000000000000022
21212121212121212121212121212122
---
00000000000000000000000000000100
  000000000000000000000000000000.01
---
00000000000000000000000000000101
22002200220022002200220022002201
---
00000000000000000000000000000102
11220112201122011220112201122012
---
00000000000000000000000000000110
 2020202020202020202020202020202.1
---
00000000000000000000000000000111
20220220220220220220220220220221
---
00000000000000000000000000000112
01221001221001221001221001221002
---
00000000000000000000000000000120
 2101210121012101210121012101210.2
---
00000000000000000000000000000121
22102210221022102210221022102211
---
00000000000000000000000000000122
22110201001120212211020100112022
---
00000000000000000000000000000200
  111111111111111111111111111111.12
---
00000000000000000000000000000201
20122001102100221120122001102101
---
00000000000000000000000000000202
22112211221122112211221122112212
---
00000000000000000000000000000210
 1021201021201021201021201021201.1
---
00000000000000000000000000000211
20221202212022120221202212022121
---
00000000000000000000000000000212
21211022012212110220122121102202
---
00000000000000000000000000000220
 2121212121212121212121212121212.2
---
00000000000000000000000000000221
12001002011022122021120010020111
---
00000000000000000000000000000222
21221221221221221221221221221222
---
00000000000000000000000000001000
   00000000000000000000000000000.001
---
00000000000000000000000000001001
00222000222000222000222000222001
---
00000000000000000000000000001002
01112220012120211100022101020112
---
00000000000000000000000000001010
 22002200220022002200220022002201

base 4

00000000000000000000000000000001
00000000000000000000000000000001
---
00000000000000000000000000000002
 0000000000000000000000000000000.2
---
00000000000000000000000000000003
22222222222222222222222222222223
---
00000000000000000000000000000010
 0000000000000000000000000000000.1
---
00000000000000000000000000000011
30303030303030303030303030303031
---
00000000000000000000000000000012
 1111111111111111111111111111111.2
---
00000000000000000000000000000013
12312312312312312312312312312313
---
00000000000000000000000000000020
  000000000000000000000000000000.02
---
00000000000000000000000000000021
20320320320320320320320320320321
---
00000000000000000000000000000022
 2121212121212121212121212121212.2
---
00000000000000000000000000000023
02322023220232202322023220232203
---
00000000000000000000000000000030
 2222222222222222222222222222222.3
---
00000000000000000000000000000031
10323010323010323010323010323011
---
00000000000000000000000000000032
 3123123123123123123123123123123.2
---
00000000000000000000000000000033
32323232323232323232323232323233
---
00000000000000000000000000000100
  000000000000000000000000000000.01
---
00000000000000000000000000000101
33003300330033003300330033003301
---
00000000000000000000000000000102
 0130130130130130130130130130130.2
---
00000000000000000000000000000103
20122330220122330220122330220123
---
00000000000000000000000000000110
 3030303030303030303030303030303.1
---
00000000000000000000000000000111
30330330330330330330330330330331
---
00000000000000000000000000000112
 1131011310113101131011310113101.2
---
00000000000000000000000000000113
31031322123310313221233103132213
---
00000000000000000000000000000120
  111111111111111111111111111111.12
---
00000000000000000000000000000121
20331130022033113002203311300221
---
00000000000000000000000000000122
 2131202131202131202131202131202.2
---
00000000000000000000000000000123
20102331220102331220102331220103
---
00000000000000000000000000000130
 1231231231231231231231231231231.3
---
00000000000000000000000000000131
03103313023002031033130230020311
---
00000000000000000000000000000132
 3131313131313131313131313131313.2

base 5

00000000000000000000000000000001
00000000000000000000000000000001
---
00000000000000000000000000000002
22222222222222222222222222222223
---
00000000000000000000000000000003
31313131313131313131313131313132
---
00000000000000000000000000000004
33333333333333333333333333333334
---
00000000000000000000000000000010
 0000000000000000000000000000000.1
---
00000000000000000000000000000011
40404040404040404040404040404041
---
00000000000000000000000000000012
32412032412032412032412032412033
---
00000000000000000000000000000013
41414141414141414141414141414142
---
00000000000000000000000000000014
23421023421023421023421023421024
---
00000000000000000000000000000020
 2222222222222222222222222222222.3
---
00000000000000000000000000000021
30423304233042330423304233042331
---
00000000000000000000000000000022
42424242424242424242424242424243
---
00000000000000000000000000000023
43014301430143014301430143014302
---
00000000000000000000000000000024
13431013431013431013431013431014
---
00000000000000000000000000000030
 3131313131313131313131313131313.2
---
00000000000000000000000000000031
43204320432043204320432043204321
---
00000000000000000000000000000032
43231042012134024323104201213403
---
00000000000000000000000000000033
11433011433011433011433011433012
---
00000000000000000000000000000034
02303433202303433202303433202304
---
00000000000000000000000000000040
 3333333333333333333333333333333.4
---
00000000000000000000000000000041
10434010434010434010434010434011
---
00000000000000000000000000000042
12434124341243412434124341243413
---
00000000000000000000000000000043
10204133214342403112301020413322
---
00000000000000000000000000000044
43434343434343434343434343434344
---
00000000000000000000000000000100
  000000000000000000000000000000.01
---
00000000000000000000000000000101
44004400440044004400440044004401
---
00000000000000000000000000000102
41122004303322440141122004303323
---
00000000000000000000000000000103
31440231440231440231440231440232
---
00000000000000000000000000000104
12334403211004123344032110041234
---
00000000000000000000000000000110
 4040404040404040404040404040404.1

base 6

00000000000000000000000000000001
00000000000000000000000000000001
---
00000000000000000000000000000002
 0000000000000000000000000000000.3
---
00000000000000000000000000000003
 0000000000000000000000000000000.2
---
00000000000000000000000000000004
  000000000000000000000000000000.13
---
00000000000000000000000000000005
44444444444444444444444444444445
---
00000000000000000000000000000010
 0000000000000000000000000000000.1
---
00000000000000000000000000000011
50505050505050505050505050505051
---
00000000000000000000000000000012
   00000000000000000000000000000.043
---
00000000000000000000000000000013
  000000000000000000000000000000.04
---
00000000000000000000000000000014
22222222222222222222222222222222.3
---
00000000000000000000000000000015
34524210313452421031345242103135
---
00000000000000000000000000000020
  000000000000000000000000000000.03
---
00000000000000000000000000000021
15024340531215024340531215024341
---
00000000000000000000000000000022
 3232323232323232323232323232323.3
---
00000000000000000000000000000023
 3333333333333333333333333333333.4
---
00000000000000000000000000000024
    0000000000000000000000000000.0213
---
00000000000000000000000000000025
53514331020412245351433102041225
---
00000000000000000000000000000030
  000000000000000000000000000000.02
---
00000000000000000000000000000031
44230540344230540344230540344231
---
00000000000000000000000000000032
  111111111111111111111111111111.13
---
00000000000000000000000000000033
 4141414141414141414141414141414.2
---
00000000000000000000000000000034
 5242103134524210313452421031345.3
---
00000000000000000000000000000035
42335251145423352511454233525115
---
00000000000000000000000000000040
   00000000000000000000000000000.013
---
00000000000000000000000000000041
20543205432054320543205432054321
---
00000000000000000000000000000042
 5312150243405312150243405312150.3
---
00000000000000000000000000000043
   00000000000000000000000000000.012
---
00000000000000000000000000000044
  414141414141414141414141414141.43
---
00000000000000000000000000000045
24045443151011240454431510112405
---
00000000000000000000000000000050
 4444444444444444444444444444444.5

base 7

00000000000000000000000000000001
00000000000000000000000000000001
---
00000000000000000000000000000002
33333333333333333333333333333334
---
00000000000000000000000000000003
44444444444444444444444444444445
---
00000000000000000000000000000004
51515151515151515151515151515152
---
00000000000000000000000000000005
54125412541254125412541254125413
---
00000000000000000000000000000006
55555555555555555555555555555556
---
00000000000000000000000000000010
x0000000000000000000000000000000.1
---
00000000000000000000000000000011
60606060606060606060606060606061
---
00000000000000000000000000000012
13613613613613613613613613613614
---
00000000000000000000000000000013
62046204620462046204620462046205
---
00000000000000000000000000000014
11623550431162355043116235504312
---
00000000000000000000000000000015
62626262626262626262626262626263
---
00000000000000000000000000000016
21035245631421035245631421035246
---
00000000000000000000000000000020
x3333333333333333333333333333333.4
---
00000000000000000000000000000021
63506350635063506350635063506351
---
00000000000000000000000000000022
63636363636363636363636363636364
---
00000000000000000000000000000023
64055232026114346405523202611435
---
00000000000000000000000000000024
41641641641641641641641641641642
---
00000000000000000000000000000025
42642642642642642642642642642643
---
00000000000000000000000000000026
64356435643564356435643564356436
---
00000000000000000000000000000030
 4444444444444444444444444444444.5
---
00000000000000000000000000000031
40645260214064526021406452602141
---
00000000000000000000000000000032
20625113436460415532302062511344
---
00000000000000000000000000000033
64646464646464646464646464646465
---
00000000000000000000000000000034
65016501650165016501650165016502
---
00000000000000000000000000000035
44016122650544016122650544016123
---
00000000000000000000000000000036
03425651203425651203425651203426
---
00000000000000000000000000000040
x51515151515151515151515151515152
---
00000000000000000000000000000041
11306521130652113065211306521131
---
00000000000000000000000000000042
65236523652365236523652365236524

base 8

00000000000000000000000000000001
00000000000000000000000000000001
---
00000000000000000000000000000002
 0000000000000000000000000000000.4
---
00000000000000000000000000000003
52525252525252525252525252525253
---
00000000000000000000000000000004
 0000000000000000000000000000000.2
---
00000000000000000000000000000005
63146314631463146314631463146315
---
00000000000000000000000000000006
 5252525252525252525252525252525.4
---
00000000000000000000000000000007
66666666666666666666666666666667
---
00000000000000000000000000000010
 0000000000000000000000000000000.1
---
00000000000000000000000000000011
70707070707070707070707070707071
---
00000000000000000000000000000012
 1463146314631463146314631463146.4
---
00000000000000000000000000000013
42721350564272135056427213505643
---
00000000000000000000000000000014
 2525252525252525252525252525252.6
---
00000000000000000000000000000015
73047304730473047304730473047305
---
00000000000000000000000000000016
 3333333333333333333333333333333.4
---
00000000000000000000000000000017
73567356735673567356735673567357
---
00000000000000000000000000000020
  000000000000000000000000000000.04
---
00000000000000000000000000000021
74170360741703607417036074170361
---
00000000000000000000000000000022
 4343434343434343434343434343434.4
---
00000000000000000000000000000023
32745032745032745032745032745033
---
00000000000000000000000000000024
 4631463146314631463146314631463.2
---
00000000000000000000000000000025
74747474747474747474747474747475
---
00000000000000000000000000000026
 1350564272135056427213505642721.4
---
00000000000000000000000000000027
51572336467515723364675157233647
---
00000000000000000000000000000030
 5252525252525252525252525252525.3
---
00000000000000000000000000000031
27024365605075341217270243656051
---
00000000000000000000000000000032
 5423542354235423542354235423542.4
---
00000000000000000000000000000033
22755022755022755022755022755023
---
00000000000000000000000000000034
 5555555555555555555555555555555.6
---
00000000000000000000000000000035
10647562604323671302151734541065
---
00000000000000000000000000000036
 5673567356735673567356735673567.4

base 9

00000000000000000000000000000001
00000000000000000000000000000001
---
00000000000000000000000000000002
44444444444444444444444444444445
---
00000000000000000000000000000003
 0000000000000000000000000000000.3
---
00000000000000000000000000000004
66666666666666666666666666666667
---
00000000000000000000000000000005
71717171717171717171717171717172
---
00000000000000000000000000000006
 4444444444444444444444444444444.6
---
00000000000000000000000000000007
63763763763763763763763763763764
---
00000000000000000000000000000008
77777777777777777777777777777778
---
00000000000000000000000000000010
 0000000000000000000000000000000.1
---
00000000000000000000000000000011
80808080808080808080808080808081
---
00000000000000000000000000000012
64815648156481564815648156481565
---
00000000000000000000000000000013
 2222222222222222222222222222222.3
---
00000000000000000000000000000014
26826826826826826826826826826827
---
00000000000000000000000000000015
31831831831831831831831831831832
---
00000000000000000000000000000016
 3535353535353535353535353535353.6
---
00000000000000000000000000000017
83838383838383838383838383838384
---
00000000000000000000000000000018
84210467842104678421046784210468
---
00000000000000000000000000000020
 4444444444444444444444444444444.5
---
00000000000000000000000000000021
61370846561370846561370846561371
---
00000000000000000000000000000022
84848484848484848484848484848485
---
00000000000000000000000000000023
 1251251251251251251251251251251.3
---
00000000000000000000000000000024
76852768527685276852768527685277
---
00000000000000000000000000000025
54265773818542657738185426577382
---
00000000000000000000000000000026
 5555555555555555555555555555555.6
---
00000000000000000000000000000027
13856750321385675032138567503214
---
00000000000000000000000000000028
57857857857857857857857857857858
---
00000000000000000000000000000030
  000000000000000000000000000000.03
---
00000000000000000000000000000031
60860860860860860860860860860861
---
00000000000000000000000000000032
12148617674027121486176740271215
---
00000000000000000000000000000033
 6262626262626262626262626262626.3

base 10

00000000000000000000000000000001
00000000000000000000000000000001
---
00000000000000000000000000000002
 0000000000000000000000000000000.5
---
00000000000000000000000000000003
66666666666666666666666666666667
---
00000000000000000000000000000004
  000000000000000000000000000000.25
---
00000000000000000000000000000005
 0000000000000000000000000000000.2
---
00000000000000000000000000000006
 3333333333333333333333333333333.5
---
00000000000000000000000000000007
42857142857142857142857142857143
---
00000000000000000000000000000008
   00000000000000000000000000000.125
---
00000000000000000000000000000009
88888888888888888888888888888889
---
00000000000000000000000000000010
 0000000000000000000000000000000.1
---
00000000000000000000000000000011
90909090909090909090909090909091
---
00000000000000000000000000000012
  666666666666666666666666666666.75
---
00000000000000000000000000000013
76923076923076923076923076923077
---
00000000000000000000000000000014
 1428571428571428571428571428571.5
---
00000000000000000000000000000015
 3333333333333333333333333333333.4
---
00000000000000000000000000000016
    0000000000000000000000000000.0625
---
00000000000000000000000000000017
94117647058823529411764705882353
---
00000000000000000000000000000018
 4444444444444444444444444444444.5
---
00000000000000000000000000000019
68421052631578947368421052631579
---
00000000000000000000000000000020
  000000000000000000000000000000.05
---
00000000000000000000000000000021
80952380952380952380952380952381
---
00000000000000000000000000000022
 5454545454545454545454545454545.5
---
00000000000000000000000000000023
43478260869565217391304347826087
---
00000000000000000000000000000024
   33333333333333333333333333333.375
---
00000000000000000000000000000025
  000000000000000000000000000000.04
---
00000000000000000000000000000026
 8461538461538461538461538461538.5
---
00000000000000000000000000000027
62962962962962962962962962962963
---
00000000000000000000000000000028
  714285714285714285714285714285.75
---
00000000000000000000000000000029
20689655172413793103448275862069
---
00000000000000000000000000000030
 6666666666666666666666666666666.7

base 30

00000000000000000000000000000001
00000000000000000000000000000001
---
00000000000000000000000000000002
 0000000000000000000000000000000.f
---
00000000000000000000000000000003
 0000000000000000000000000000000.a
---
00000000000000000000000000000004
  000000000000000000000000000000.7f
---
00000000000000000000000000000005
 0000000000000000000000000000000.6
---
00000000000000000000000000000006
 0000000000000000000000000000000.5
---
00000000000000000000000000000007
lcplcplcplcplcplcplcplcplcplcpld
---
00000000000000000000000000000008
   00000000000000000000000000000.3mf
---
00000000000000000000000000000009
  000000000000000000000000000000.3a
---
0000000000000000000000000000000a
 0000000000000000000000000000000.3
---
0000000000000000000000000000000b
gar85dj2logar85dj2logar85dj2logb
---
0000000000000000000000000000000c
  000000000000000000000000000000.2f
---
0000000000000000000000000000000d
96rkn296rkn296rkn296rkn296rkn297
---
0000000000000000000000000000000e
 lcplcplcplcplcplcplcplcplcplcpl.f
---
0000000000000000000000000000000f
 0000000000000000000000000000000.2
---
0000000000000000000000000000000g
    0000000000000000000000000000.1q7f
---
0000000000000000000000000000000h
s71ms71ms71ms71ms71ms71ms71ms71n
---
0000000000000000000000000000000i
  000000000000000000000000000000.1k
---
0000000000000000000000000000000j
cisciscisciscisciscisciscisciscj
---
0000000000000000000000000000000k
  000000000000000000000000000000.1f
---
0000000000000000000000000000000l
 48h48h48h48h48h48h48h48h48h48h4.a
---
0000000000000000000000000000000m
 5dj2logar85dj2logar85dj2logar85.f
---
0000000000000000000000000000000n
93rbm56fjgskq2i7onead193rbm56fjh
---
0000000000000000000000000000000o
   00000000000000000000000000000.17f
---
0000000000000000000000000000000p
  000000000000000000000000000000.16
---
0000000000000000000000000000000q
 idpbg4idpbg4idpbg4idpbg4idpbg4i.f
---
0000000000000000000000000000000r
   00000000000000000000000000000.13a
---
0000000000000000000000000000000s
  lcplcplcplcplcplcplcplcplcplcp.mf
---
0000000000000000000000000000000t
ssssssssssssssssssssssssssssssst
---
00000000000000000000000000000010
 0000000000000000000000000000000.1


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© Scott Sherman 1999