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

1,1

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, ...

Links

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

Example

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

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 *)

Crossrefs

Sequence in context: A239309 A077073 A307126 * A199602 A324057 A106315

Adjacent sequences: A191471 A191472 A191473 * A191475 A191476 A191477

Keyword

nonn

Author

Zak Seidov, Aug 28 2012

Extensions

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

Status

approved