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A004520 Generalized nim sum n + n in base 10. 19
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 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=0..76.

David Applegate, Marc LeBrun and N. J. A. Sloane, Carryless Arithmetic (I): The Mod 10 Version.

Index entries for sequences related to carryless arithmetic

Index entries for sequences related to Nim-sums

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 *)

CROSSREFS

When sorted and duplicates removed, gives A014263. - N. J. A. Sloane, Aug 03 2010

Sequence in context: A243590 A169933 A113603 * A169918 A169916 A073909

Adjacent sequences:  A004517 A004518 A004519 * A004521 A004522 A004523

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Robert G. Wilson v, Aug 23 2010

STATUS

approved

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Last modified February 18 23:26 EST 2018. Contains 299330 sequences. (Running on oeis4.)