Monday, September 12, 2016

[sgnuxiuo] Multiplication table in various bases

Omitting multipliers 0 and 1 because they are trivial (which makes the entire base 2 multiplication table trivial).  Source code in Perl.  Heavy lifting is done by "bc".

There are some patterns visible between bases.

Base 3

*2*
2112
*2*

Base 4

*23*
210122
312213
*23*

Base 5

*234*
2411132
31114223
41322314
*234*

Base 6

*2345*
241012142
3101320233
4122024324
5142332415
*2345*

Base 7

*23456*
2461113152
36121521243
411152226334
513212634425
615243342516
*23456*

Base 8

*234567*
246101214162
3611141722253
41014202430344
51217243136435
61422303644526
71625344352617
*234567*

Base 9

*2345678*
2468111315172
361013162023263
481317222631354
5111622273338445
6132026334046536
7152331384654627
8172635445362718
*2345678*

Base 10

*23456789*
246810121416182
3691215182124273
48121620242832364
510152025303540455
612182430364248546
714212835424956637
816243240485664728
918273645546372819
*23456789*

Base 11

*23456789A*
2468A11131517192
3691114171A2225283
4811151922262A33374
5A14192328323741465
6111722283339444A556
7131A263239455158647
815222A3744515966738
9172533414A586674829
A192837465564738291A
*23456789A*

Base 12

*23456789AB*
2468A10121416181A2
36910131619202326293
481014182024283034384
5A131821262B343942475
6101620263036404650566
71219242B364148535A657
8142028344048546068748
9162330394653606976839
A18263442505A68768492A
B1A2938475665748392A1B
*23456789AB*

Base 13

*23456789ABC*
2468AC11131517191B2
369C1215181B2124272A3
48C13171B22262A3135394
5A12171C242931363B43485
6C151B242A3339424851576
711182229333A444B555C667
8131B263139444C57626A758
915212A36424B57636C78849
A1724313B4855626C798693A
B19273543515C6A788694A2B
C1B2A39485766758493A2B1C
*23456789ABC*

Base 14

*23456789ABCD*
2468AC10121416181A1C2
369C1114171A1D2225282B3
48C12161A2024282C32363A4
5A11161B22272C33383D44495
6C141A222830363C444A52586
71017202730374047505760677
8121A242C364048525A646C768
9141D28333C47525B66717A859
A16222C3844505A66727C8894A
B1825323D4A5764717C8996A3B
C1A28364452606C7A8896A4B2C
D1C2B3A495867768594A3B2C1D
*23456789ABCD*

Base 15

*23456789ABCDE*
2468ACE11131517191B1D2
369C101316191C202326292C3
48C1115191D22262A2E33373B4
5A10151A20252A30353A40454A5
6C131920262C333940464C53596
7E161D252C343B434A525961687
81119222A333B444C555D666E778
9131C263039434C566069737C869
A15202A35404A55606A75808A95A
B17232E3A46525D6975818C98A4B
C192633404C596673808C99A6B3C
D1B29374553616E7C8A98A6B4C2D
E1D2C3B4A5968778695A4B3C2D1E
*23456789ABCDE*

Base 16

*23456789ABCDEF*
2468ACE10121416181A1C1E2
369CF1215181B1E2124272A2D3
48C1014181C2024282C3034383C4
5AF14191E23282D32373C41464B5
6C12181E242A30363C42484E545A6
7E151C232A31383F464D545B62697
810182028303840485058606870788
9121B242D363F48515A636C757E879
A141E28323C46505A646E78828C96A
B16212C37424D58636E79848F9AA5B
C1824303C4854606C7884909CA8B4C
D1A2734414E5B6875828F9CA9B6C3D
E1C2A38465462707E8C9AA8B6C4D2E
F1E2D3C4B5A69788796A5B4C3D2E1F
*23456789ABCDEF*