A258127 Smallest k such that Sum_{i=0..k} binomial(n,i) is prime, or a(n)=0 if there is no such k.

1, 1, 2, 1, 4, 1, 2, 2, 0, 1, 2, 1, 4, 4, 6, 1, 16, 1, 2, 2, 4, 1, 2, 6, 8, 16, 2, 1, 0, 1, 4, 6, 0, 0, 2, 1, 0, 0, 0, 1, 0, 1, 2, 2, 0, 1, 2, 10, 0, 48, 2, 1, 36, 20, 6, 2, 8, 1, 10, 1, 16, 13, 2, 2, 0, 1, 0, 2, 0, 1, 2, 1, 0, 0, 2, 2, 0, 1, 8, 74, 64, 1, 16

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 1,2,4,6,16,48,74,...

at positions 1,3,5,15,17,50,80,...

Links

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

Crossrefs

Cf. A007318, A258126.

Programs

PARI

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

Formula

a(n) <= n-1.

Extensions

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