

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 Nimvarieties and Binomial Coefficients, INTEGERS 7 (2)(2007), #A14.
E. E. Kummer, Über die Ergänzungssätze zu den allgemeinen Reciprocitätsgesetzen, J. Reine Angew. Math. 44 (1852), 93146.


FORMULA

2Binomial(2*A241757(n), a(n)). Indeed, from the Kummer theorem (see reference) 2^tBinomial(n,x) if and only if in adding x and nx 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



