A256163 Odd numbers m such that for all 2^k < m the numbers m + 2^k, m - 2^k, m*2^k + 1, and m*2^k - 1 are composite, with k >= 1.

1, 7913, 8923, 24943, 34009, 35437, 42533, 52783, 60113, 83437, 100727, 105953, 116437, 120521, 126631, 132211, 133241, 137171, 145589, 164729, 172331, 181645, 183671, 192173, 196633, 199513, 203069, 204013, 215113, 215279, 218503, 220523, 253519, 254329, 254587

Offset: 1

Author

Arkadiusz Wesolowski, Mar 17 2015

Keywords

• nonn

Links

• Felix Fröhlich, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006285, A076335.

Subsequence of A255967.

A256237 gives the primes.

Programs

Magma

lst:=[]; for n in [1..254587 by 2] do t:=0; k:=0; while 2^k lt n do if IsPrime(n-2^k) or IsPrime(n+2^k) or IsPrime(n*2^k-1) or IsPrime(n*2^k+1) 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] && !PrimeQ[m * pow - 1] && !PrimeQ[m * pow + 1], pow *= 2]; pow > m]]; Select[Range[300000], q] (* Amiram Eldar, Jul 19 2025 *)

PARI

for(n=1, 1e6, if(n%2==1, k=0; prim=0; while(2^k < n, if(ispseudoprime(n+2^k) || ispseudoprime(n-2^k) || ispseudoprime(n*2^k+1) || ispseudoprime(n*2^k-1), prim++; break({1})); k++); if(prim==0, print1(n, ", ")))) \\ Felix Fröhlich, Apr 01 2015