A365475 - OEIS

%I #7 Sep 04 2023 12:26:45

%S 3,5,17,17,257,257,257,257,65537,65537,65537,65537,65537,65537,65537,

%T 65537,4398054899713,4398054899713,4398054899713,1125899915231233,

%U 1125899915231233,1125899915231233,1125899915231233,2251799847239681,2251799847239681,1152921513196781569,1152921513196781569

%N a(n) is the first odd prime p such that A000120((2^n-1)*p) = n * A000120(p).

%C a(n) is the first odd prime p such that between any two 1's in the base-2 representation of p there are at least n-1 0's.

%H Robert Israel, <a href="/A365475/b365475.txt">Table of n, a(n) for n = 1..1000</a>

%e a(3) = 17 because A000120((2^3-1) * 17) = A000120(119) = 6 = 3 * A000120(17).

%p f:= proc(m) local S,d,j,r,q;

%p   S[0]:= [1];

%p   for d from 1 do

%p     S[d]:= NULL;

%p     for j from 0 to d-m do

%p       for r in S[j] do

%p         q:= r + 2^d;

%p         if isprime(q) then return q fi;

%p         S[d]:= S[d],q;

%p       od;

%p     od;

%p     S[d]:= [S[d]];

%p   od;

%p end proc:

%p map(f, [$1..30]);

%Y Cf. A000120.

%K nonn,base

%O 1,1

%A _Robert Israel_, Sep 04 2023