A191474 Smallest prime q such that q + prime(n) is a power of 2.

2, 5, 3, 549755813881, 5, 3, 47, 13, 41, 3, 97, 2011, 23, 536870869, 17, 11, 5, 3, 61, 953, 439, 433, 173, 167, 31, 67108763, 409, 149, 19, 911, 140737488355201, 16253, 887, 373, 107, 2147483497, 32611, 349, 89, 83, 3917, 331, 16193, 2096959, 59, 313, 33554221

Offset: 1

Author

Zak Seidov, Aug 28 2012

Keywords

• nonn

Comments

Corresponding exponents of 2: 2, 3, 3, 39, 4, 4, 6, 5, 6, 5, 7, 11, 6, 29, 6, 6, 6, 6, 7, 10, 9, 9, 8, 8, 7, 1, 9, 8, 7, 10, 47, 14, 10, 9, 8, 31, 15, 9, 8, 8, 12, 9, 14, 21, 8, 9, 1, ...

Examples

			2 + 2 = 2^2,
3 + 5 = 2^3,
5 + 3 = 2^3,
7 + 549755813881 = 2^39,
11 + 5 = 2^4.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..285

Programs

Maple

f:= proc(n) local p,m,t,q;
  p:= ithprime(n);
  for t from ilog2(p) do
    q:= 2^t - p;
    if isprime(q) then return q fi;
  od;
end proc:
map(f, [$1..50]); # Robert Israel, Dec 23 2020

Mathematica

f[p_] := NestWhile[2 # &, 2^Ceiling[Log[2, p]], ! PrimeQ[# - p] &] - p;
f /@ Prime@Range@47 (* David Trimas, Jul 30 2023 *)

Extensions

a(26) corrected by Robert Israel, Dec 23 2020