A365475 a(n) is the first odd prime p such that A000120((2^n-1)*p) = n * A000120(p).

3, 5, 17, 17, 257, 257, 257, 257, 65537, 65537, 65537, 65537, 65537, 65537, 65537, 65537, 4398054899713, 4398054899713, 4398054899713, 1125899915231233, 1125899915231233, 1125899915231233, 1125899915231233, 2251799847239681, 2251799847239681, 1152921513196781569, 1152921513196781569

Offset: 1

Author

Robert Israel, Sep 04 2023

Keywords

• nonn
• base

Comments

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.

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000120.

Programs

Maple

f:= proc(m) local S,d,j,r,q;
  S[0]:= [1];
  for d from 1 do
    S[d]:= NULL;
    for j from 0 to d-m do
      for r in S[j] do
        q:= r + 2^d;
        if isprime(q) then return q fi;
        S[d]:= S[d],q;
      od;
    od;
    S[d]:= [S[d]];
  od;
end proc:
map(f, [$1..30]);