A274589 Primes not of the form (prime+1)*2^k-1 with k>=1.

2, 3, 13, 17, 19, 29, 37, 41, 43, 53, 61, 67, 73, 89, 97, 101, 103, 109, 113, 131, 137, 139, 149, 157, 163, 173, 181, 193, 197, 199, 211, 229, 233, 241, 251, 257, 269, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 349, 353, 367

Offset

1,1

Comments

A permutation of A057026 (excluding the zeros, e.g., A057026(254601) = 0).

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

103 = (51+1)*2^1-1 = (25+1)*2^2-1 = (12+1)*2^3-1, the numbers 51, 25 and 12 are not primes, so 103 is in the sequence.
71 = (35+1)*2^1-1 = (17+1)*2^2-1 = (8+1)*2^3-1, the number 17 is prime, so 71 is not in the sequence.

Maple

filter := proc(n) local k;
  if not isprime(n) then return false fi;
  for k from 1 to padic:-ordp(n+1, 2) do
     if isprime((n+1)/2^k-1) then return false
     fi
  od:
  true
end proc:
select(filter, [2, seq(i, i=3..1000, 2)]); # Robert Israel, Jun 29 2016

Crossrefs

Cf. A057026, A266233 (complement with respect to A000040).

Sequence in context: A059670 A038975 A059456 * A019394 A048704 A045340

Adjacent sequences: A274586 A274587 A274588 * A274590 A274591 A274592

Keyword

nonn

Author

Gionata Neri, Jun 29 2016

Status

approved