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URL: https://oeis.org/A241758

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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
OFFSET
1,1
LINKS
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
Sequence in context: A114508 A243366 A139023 * A074808 A173620 A319920
KEYWORD
nonn,base
AUTHOR
Vladimir Shevelev, Apr 28 2014
EXTENSIONS
More terms from Peter J. C. Moses, Apr 29 2014
STATUS
approved