cp's OEIS Frontend

A118957 Numbers of the form 2^k + p, where p is a prime less than 2^k.

%I A118957 #24 Feb 23 2025 04:51:52
%S A118957 6,7,10,11,13,15,18,19,21,23,27,29,34,35,37,39,43,45,49,51,55,61,63,
%T A118957 66,67,69,71,75,77,81,83,87,93,95,101,105,107,111,117,123,125,130,131,
%U A118957 133,135,139,141,145,147,151,157,159,165,169,171,175,181,187,189,195,199
%N A118957 Numbers of the form 2^k + p, where p is a prime less than 2^k.
%F A118957 A118952(a(n)) = 1.
%p A118957 isA118957 := proc(n)
%p A118957     local twok,p ;
%p A118957     twok := 1 ;
%p A118957     while twok < n-1 do
%p A118957         p := n-twok ;
%p A118957         if isprime(p) and p < twok then
%p A118957             return true;
%p A118957         end if;
%p A118957         twok := twok*2 ;
%p A118957     end do:
%p A118957     return false;
%p A118957 end proc:
%p A118957 for n from 1 to 200 do
%p A118957     if isA118957(n) then
%p A118957         printf("%d,",n) ;
%p A118957     end if;
%p A118957 end do: # _R. J. Mathar_, Feb 27 2015
%t A118957 okQ[n_] := Module[{k, p}, For[k = Ceiling[Log[2, n]], k>1, k--, p = n-2^k; If[2 <= p < 2^k && PrimeQ[p], Return[True]]]; False]; Select[Range[200], okQ] (* _Jean-François Alcover_, Mar 11 2019 *)
%o A118957 (PARI) is(n)=isprime(n-2^logint(n,2)) \\ _Charles R Greathouse IV_, Sep 01 2015; edited Jan 24 2024
%o A118957 (Python)
%o A118957 from sympy import primepi
%o A118957 def A118957(n):
%o A118957     def bisection(f,kmin=0,kmax=1):
%o A118957         while f(kmax) > kmax: kmax <<= 1
%o A118957         kmin = kmax >> 1
%o A118957         while kmax-kmin > 1:
%o A118957             kmid = kmax+kmin>>1
%o A118957             if f(kmid) <= kmid:
%o A118957                 kmax = kmid
%o A118957             else:
%o A118957                 kmin = kmid
%o A118957         return kmax
%o A118957     def f(x): return n+x-sum(primepi(min(x-(m:=1<<k),m-1)) for k in range(x.bit_length()))
%o A118957     return bisection(f,n,n) # _Chai Wah Wu_, Feb 23 2025
%Y A118957 Complement of A118956; subsequence of A118955.
%Y A118957 Cf. A118952, A118958, A156695.
%K A118957 nonn
%O A118957 1,1
%A A118957 _Reinhard Zumkeller_, May 07 2006