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A004520
Generalized nim sum n + n in base 10.
21
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
OFFSET
0,2
COMMENTS
a(n) = n + n in carryless arithmetic mod 10. - N. J. A. Sloane, Jul 23 2010.
REFERENCES
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.
FORMULA
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.
MATHEMATICA
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 *)
PROG
(Python)
def A004520(n):
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
CROSSREFS
When sorted and duplicates removed, gives A014263. - N. J. A. Sloane, Aug 03 2010
Sequence in context: A243590 A169933 A113603 * A169918 A169916 A073909
KEYWORD
nonn,base,easy
EXTENSIONS
More terms from Robert G. Wilson v, Aug 23 2010
STATUS
approved