OFFSET
1,1
LINKS
Peter J. C. Moses, Table of n, a(n) for n = 1..10000
Aviezri Fraenkel and Alex Kontorovich, The Sierpiński Sieve of Nim-varieties and Binomial Coefficients, INTEGERS 7 (2)(2007), #A14.
E. E. Kummer, Über die Ergänzungssätze zu den allgemeinen Reciprocitätsgesetzen, J. Reine Angew. Math. 44 (1852), 93-146.
FORMULA
2||Binomial(2*A241757(n), a(n)). Indeed, from the Kummer theorem (see reference) 2^t||Binomial(n,x) if and only if in adding x and n-x in binary we have exactly t carries. A proof of the Kummer theorem in arbitrary base one can find in [Fraenkel & Kontorovich].
EXAMPLE
a(2)=5, since A241757(2)=22=5+17, and in binary in sum of 101+10001 involves only one carry.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Vladimir Shevelev, Apr 28 2014
EXTENSIONS
More terms from Peter J. C. Moses, Apr 29 2014
STATUS
approved