cp's OEIS Frontend

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.

%I A255967 #22 Jul 19 2025 10:12:48
%S A255967 1,1973,3181,3967,4889,5617,7747,7913,8363,8587,8923,11437,11993,
%T A255967 12517,13285,13973,14101,14231,14489,16117,16769,16849,18391,18611,
%U A255967 19583,19819,21289,21683,21701,21893,22147,22817,22949,23651,24943,25829,27197,27437
%N 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.
%C A255967 Odd numbers m such that for all 2^k < m the numbers m + 2^k and m - 2^k are composite, with k >= 1.
%H A255967 Amiram Eldar, <a href="/A255967/b255967.txt">Table of n, a(n) for n = 1..10000</a>
%t A255967 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 *)
%o A255967 (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;
%o A255967 (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
%Y A255967 Cf. A076335.
%Y A255967 Subsequence of A006285. Supersequence of A256163.
%Y A255967 A153352 gives the primes.
%K A255967 nonn
%O A255967 1,2
%A A255967 _Arkadiusz Wesolowski_, Mar 12 2015