A258483 Numbers n such that partial sums of the n-th row of the Pascal triangle (A007318) are all nonprime.

0, 9, 29, 33, 34, 37, 38, 39, 41, 45, 49, 65, 67, 69, 73, 74, 77, 85, 86, 92, 97, 98, 101, 105, 113, 114, 115, 117, 118, 121, 129, 133, 134, 137, 139, 141, 145, 146, 151, 154, 155, 158, 160, 161, 164, 165, 170, 173, 177, 182, 185, 186, 193, 194, 195, 199, 202, 205, 206, 209, 213, 214, 225, 227, 229, 230, 234, 241, 247, 257, 258, 259, 261, 263, 265, 266, 269, 272, 273, 277, 281

Offset

0,2

Comments

It appears that a(n) ~ c*n, as n goes to infinity, where c is constant < 2.17. For heuristic argument, see Robert Israel link.

Links

Peter J. C. Moses, Table of n, a(n) for n = 0..2499

Robert Israel, Re: a surprising property, SeqFan list, Jun 01 2015.

Maple

T:= <1>:
res:= 0:
for n from 1 to 1000 do
  T:= <1, T[1..-2] + T[2..-1], 2^n>;
  if not ormap(isprime, T) then res:= res, n fi
od:
res; # Robert Israel, Jun 04 2015

Prog

(PARI) isok(n) = {my(s = 0); for (k=0, n, s += binomial(n, k); if (isprime(s), return (0))); return (1); } \\ Michel Marcus, May 31 2015

Crossrefs

Cf. A007318, A008949, A258126, A258127.

Sequence in context: A041154 A024121 A205144 * A044976 A002642 A032700

Adjacent sequences: A258480 A258481 A258482 * A258484 A258485 A258486

Keyword

nonn

Author

Vladimir Shevelev, May 31 2015

Status

approved