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A169916
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Squares in carryless arithmetic mod 10 with addition and multiplication of digits both defined to be addition mod 10.
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3
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0, 2, 4, 6, 8, 0, 2, 4, 6, 8, 220, 242, 264, 286, 208, 220, 242, 264, 286, 208, 440, 462, 484, 406, 428, 440, 462, 484, 406, 428, 660, 682, 604, 626, 648, 660, 682, 604, 626, 648, 880, 802, 824, 846, 868, 880, 802, 824, 846, 868, 0, 22, 44, 66, 88, 0, 22, 44, 66, 88, 220, 242
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OFFSET
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0,2
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COMMENTS
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The rules of arithmetic used in A169916, A169917, A169918 have very strange consequences. Many of the familiar laws fail. For instance, the arithmetic in A169916 is not associative: 10*(9*2) = 10*1 = 21 != (10*9)*2 = 9*2 = 1.
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LINKS
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Table of n, a(n) for n=0..61.
Index entries for sequences related to carryless arithmetic
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FORMULA
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a(n)=a(n') if respective digits of n and n' differ by 0 or 5. In particular, a(10k+m) = a(10k+m+5) if 0 <= m <= 4.
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EXAMPLE
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a(16) = 16*16 = 242:
....16
....16
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....72 (6*6 = 6+6 mod 10 = 2, 6*1 = 6+1 mod 10 = 7)
...27.
------
...242
------
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PROG
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(PARI) A169916(n)={u=vector(#n=digits(n), i, 1); n=apply(d->n+d*u, n)%10; sum(i=0, 2*#n-2, sum(j=max(1, #n-i), min(2*#n-1-i, #n), n[2*#n-i-j][j])%10*10^i)} \\ M. F. Hasler, Mar 26 2015
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CROSSREFS
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The four versions are A059729, A169916, A169917, A169918.
Sequence in context: A113603 A004520 A169918 * A073909 A036211 A127353
Adjacent sequences: A169913 A169914 A169915 * A169917 A169918 A169919
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KEYWORD
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nonn,base
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AUTHOR
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David Applegate, Marc LeBrun and N. J. A. Sloane, Jul 20 2010
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STATUS
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approved
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