A241758 Smallest prime in representation 2*A241757(n) by sum of two primes, the adding of which in binary requires only one carry.

2, 5, 13, 5, 17, 17, 5, 17, 5, 5, 13, 17, 5, 13, 5, 17, 37, 17, 5, 13, 17, 17, 29, 37, 41, 5, 5, 17, 13, 5, 13, 17, 5, 37, 41, 17, 5, 73, 5, 89, 13, 97, 5, 13, 17, 37, 41, 29, 137, 5, 5, 41, 5, 41, 13, 193, 5, 5, 17, 193, 17, 17, 37, 41, 37, 97, 53, 73, 53, 5

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

Cf. A241757, A241405.

Sequence in context: A114508 A243366 A139023 * A173620 A319920 A166134

Adjacent sequences: A241755 A241756 A241757 * A241759 A241760 A241761

Keyword

nonn,base

Author

Vladimir Shevelev, Apr 28 2014

Extensions

More terms from Peter J. C. Moses, Apr 29 2014

Status

approved