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A241758 Smallest prime in representation 2*A241757(n) by sum of two primes, the adding of which in binary requires only one carry. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A243366 A164793 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

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Last modified July 17 18:47 EDT 2019. Contains 325109 sequences. (Running on oeis4.)