A258483 Numbers n such that partial sums of the n-th row of Pascal's 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

Author

Vladimir Shevelev, May 31 2015

Keywords

• nonn

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.

Crossrefs

Cf. A007318, A008949, A258126, A258127.

Programs

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

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