A258126 Smallest prime of the form Sum_{i=0..k} binomial(n,i), or a(n)=0 if there is no such a prime.

2, 3, 7, 5, 31, 7, 29, 37, 0, 11, 67, 13, 1093, 1471, 9949, 17, 131071, 19, 191, 211, 7547, 23, 277, 190051, 1807781, 61450327, 379, 29, 0, 31, 36457, 1149017, 0, 0, 631, 37, 0, 0, 0, 41, 0, 43, 947, 991, 0, 47, 1129, 8682997471, 0, 1125899906842573, 1327, 53

Offset: 1

Author

Vladimir Shevelev, May 21 2015

Keywords

• nonn

Comments

a(n)=0 for n=9,29,33,34,37,38,39,41,45,49,...;

records a(n) are on the positions: 1,2,3,5,8,11,13,14,15,17,24,25,26,48,50,...

Mersenne primes a(n) = 2^n-1 are at positions 2,3,5,17,...

Links

• Peter J. C. Moses, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A007318, A258127.

Programs

PARI

a(n) = {my(k = 0); while(! isprime(p=sum(i=0, k, binomial(n,i))), k++; if ((k>n) && !isprime(binomial(n,k)), return (0);)); p;} \\ Michel Marcus, May 23 2015

Formula

a(n) <= 2^n-1.

Extensions

More terms from Peter J. C. Moses, May 21 2015