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A004520
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Generalized nim sum n + n in base 10.
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21
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0, 2, 4, 6, 8, 0, 2, 4, 6, 8, 20, 22, 24, 26, 28, 20, 22, 24, 26, 28, 40, 42, 44, 46, 48, 40, 42, 44, 46, 48, 60, 62, 64, 66, 68, 60, 62, 64, 66, 68, 80, 82, 84, 86, 88, 80, 82, 84, 86, 88, 0, 2, 4, 6, 8, 0, 2, 4, 6, 8, 20, 22, 24, 26, 28, 20, 22, 24, 26, 28, 40, 42, 44, 46, 48, 40, 42
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OFFSET
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0,2
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COMMENTS
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a(n) = n + n in carryless arithmetic mod 10. - N. J. A. Sloane, Jul 23 2010.
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REFERENCES
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E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982.
J. H. Conway, On Numbers and Games. Academic Press, NY, 1976.
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LINKS
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FORMULA
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Generalized nim sum m + n in base q: write m and n in base q and add mod q with no carries, e.g. 5 + 8 in base 3 = "21" + "22" = "10" = 1.
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MATHEMATICA
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carrylessAdd[m_, n_, b_] := Block[{lm = IntegerLength[m, b], ln = IntegerLength[n, b]}, mx = Max[lm, ln]; idm = IntegerDigits[m, b, mx]; idn = IntegerDigits[n, b, mx]; FromDigits[ Mod[ idm + idn, b], b]]; Table[ carrylessAdd[n, n, 10], {n, 0, 76}] (* Robert G. Wilson v, Aug 23 2010 *)
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PROG
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(Python)
return int(''.join(str(2*int(d) % 10) for d in str(n))) # Chai Wah Wu, Jun 29 2020
(PARI) a(n) = fromdigits(digits(n)%5)<<1; \\ Kevin Ryde, Dec 10 2022
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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