cp's OEIS Frontend

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.

%I A256163 #28 Jul 19 2025 10:12:44
%S A256163 1,7913,8923,24943,34009,35437,42533,52783,60113,83437,100727,105953,
%T A256163 116437,120521,126631,132211,133241,137171,145589,164729,172331,
%U A256163 181645,183671,192173,196633,199513,203069,204013,215113,215279,218503,220523,253519,254329,254587
%N 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.
%H A256163 Felix Fröhlich, <a href="/A256163/b256163.txt">Table of n, a(n) for n = 1..10000</a>
%t A256163 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 *)
%o A256163 (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;
%o A256163 (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
%Y A256163 Cf. A006285, A076335.
%Y A256163 Subsequence of A255967.
%Y A256163 A256237 gives the primes.
%K A256163 nonn
%O A256163 1,2
%A A256163 _Arkadiusz Wesolowski_, Mar 17 2015