A057676 Smallest prime q such that 2^prime(n) - q is prime.

2, 3, 3, 19, 19, 13, 13, 19, 37, 3, 19, 31, 31, 67, 127, 379, 607, 31, 19, 577, 181, 67, 97, 31, 349, 619, 97, 919, 31, 211, 577, 181, 13, 397, 31, 829, 19, 577, 577, 103, 1669, 199, 19, 31, 439, 1021, 601, 1621, 2017, 733, 3, 199, 2113, 619, 1861, 1297, 241, 967

Offset: 1

Author

Labos Elemer, Oct 19 2000

Keywords

• nonn

Examples

			For n = 4, prime(4) = 11, 2^11 = 2048, p2 = 2048-p1 is satisfied at first with prime p1 = 19 resulting in prime p2 = 2029, so a(4) = 19.
For n = 31, prime(31) = 127, p2 = 2^127-p1 is satisfied first with p1 = 577 and p2 = 170141183460469231731687303715884105151, so a(31) = 577.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..560

Crossrefs

Cf. A057662, A056206, A056208.

Programs

Mathematica

spq[n_]:=Module[{p=2,t=2^Prime[n]},While[!PrimeQ[t-p],p=NextPrime[p]];p]; Array[spq,60] (* Harvey P. Dale, Jul 13 2025 *)

PARI

a(n) = {my(p = 1 << prime(n), q = 2); while(!isprime(p - q), q = nextprime(q + 1)); q;} \\ Amiram Eldar, Feb 18 2025

Extensions

Offset corrected by Amiram Eldar, Feb 18 2025