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

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy

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

• 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

Crossrefs

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

Programs

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 *)

PARI

a(n) = fromdigits(digits(n)%5)<<1; \\ Kevin Ryde, Dec 10 2022

Python

def A004520(n):
    return int(''.join(str(2*int(d) % 10) for d in str(n))) # Chai Wah Wu, Jun 29 2020

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.

Extensions

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