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
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.
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
KEYWORD
nonn,base,easy
AUTHOR
EXTENSIONS
More terms from Robert G. Wilson v, Aug 23 2010
STATUS
approved