A255967 Odd numbers m that are neither of the form p + 2^k nor of the form p - 2^k with 2^k < m, k >= 1, and p prime.

1, 1973, 3181, 3967, 4889, 5617, 7747, 7913, 8363, 8587, 8923, 11437, 11993, 12517, 13285, 13973, 14101, 14231, 14489, 16117, 16769, 16849, 18391, 18611, 19583, 19819, 21289, 21683, 21701, 21893, 22147, 22817, 22949, 23651, 24943, 25829, 27197, 27437

Offset: 1

Author

Arkadiusz Wesolowski, Mar 12 2015

Keywords

• nonn

Comments

Odd numbers m such that for all 2^k < m the numbers m + 2^k and m - 2^k are composite, with k >= 1.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A076335.

Subsequence of A006285. Supersequence of A256163.

A153352 gives the primes.

Programs

Magma

lst:=[]; for n in [1..27437 by 2] do t:=0; k:=0; while 2^k lt n do if IsPrime(n-2^k) or IsPrime(n+2^k) then t:=1; break; end if; k+:=1; end while; if IsZero(t) then Append(~lst, n); end if; end for; lst;

Mathematica

q[m_] :=  If[EvenQ[m], False, Module[{pow = 2},While[pow < m && !PrimeQ[m - pow] && !PrimeQ[m + pow], pow *= 2]; pow > m]]; Select[Range[30000], q] (* Amiram Eldar, Jul 19 2025 *)

PARI

isok(m) = if(!(m % 2), 0, my(pow = 2); while(pow < m && !isprime(m - pow) && !isprime(m + pow), pow *= 2); pow > m); \\ Amiram Eldar, Jul 19 2025