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

1,3

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

Formula

a(n) <= n-1.

Prog

(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

Crossrefs

Cf. A007318, A258126.

Sequence in context: A100762 A059147 A091891 * A181982 A070194 A323300

Adjacent sequences: A258124 A258125 A258126 * A258128 A258129 A258130

Keyword

nonn

Author

Vladimir Shevelev, May 21 2015

Extensions

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

Status

approved