A331204 Least m > n such that 2^m - 2^n + 1 is prime.

1, 2, 3, 39, 5, 7, 8, 47, 9, 13, 14, 27, 14, 23, 17, 447, 17, 23, 20, 31, 23, 27, 34, 39, 31, 31, 29, 31, 43, 41, 32, 191, 40, 43, 49, 59, 38, 41, 42, 255, 64, 43, 65, 331, 48, 59, 62, 111, 52, 79, 53, 91, 55, 75, 61, 199, 71, 65, 86, 99, 65, 127, 74

Offset: 0

Author

Hugo Pfoertner, Jan 12 2020

Keywords

• nonn
• hard

Comments

If it exists, a(63) > 10000.

Examples

			a(0) = 1: 2^1 - 2^0 + 1 = 2 = A331205(0) is prime,
a(1) = 2: 2^2 - 2^1 + 1 = 3 = A331205(1) is prime,
a(2) = 3: 2^3 - 2^2 + 1 = 5 = A331205(2) is prime,
a(3) = 39: 2^39 - 2^3 + 1 = 549755813881 = A331205(3) is prime, whereas all smaller values of m give composite sums: 9, 25, 57, 121, 249, 505, ..., 274877906937.
		

Crossrefs

Cf. A181692, A331205 (corresponding primes).

Programs

PARI

for(n=0,62, for(m=n+1,oo, k=2^m-2^n+1; if(isprime(k), print1(m,", "); break)))