A004520 Generalized nim sum n + n in base 10.

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.

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.

R. Hinze, Concrete stream calculus: An extended study, J. Funct. Progr. 20 (5-6) (2010) 463-535, doi, Section 4.4.

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 *)

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

Adjacent sequences: A004517 A004518 A004519 * A004521 A004522 A004523

Keyword

nonn,base,easy

Author

N. J. A. Sloane

Extensions

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

Status

approved