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

Author

Vladimir Shevelev, Apr 28 2014

Keywords

• nonn
• base

Examples

			a(2)=5, since A241757(2)=22=5+17, and in binary in sum of 101+10001 involves only one carry.
		

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.

Crossrefs

Cf. A241757, A241405.

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].

Extensions

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