A032418 Numbers n such that 137 * 2^n + 1 is a prime.

3, 27, 39, 83, 203, 395, 467, 875, 1979, 6939, 13623, 22835, 56307, 81839, 197783, 224879, 261147, 523283, 533043, 2457639

Offset: 1

Author

James R. Buddenhagen

Keywords

• nonn
• hard

Examples

			137 * 2^3 + 1 = 1097 is a prime so 3 is in the sequence.
137 * 2^5 + 1 = 4385 = 5 * 877, so 5 is not in the sequence.
		

Links

• Ray Ballinger, Proth Search Page
• Ray Ballinger and Wilfrid Keller, List of primes k.2^n + 1 for k < 300
• Wilfrid Keller, List of primes k.2^n - 1 for k < 300
• Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is a prime

Programs

Mathematica

Select[Range[1000], PrimeQ[137  2^# + 1] &] (* Alonso del Arte, Apr 06 2020 *)

Extensions

3 more terms sent by Jud McCranie, Jan 15 2000 and May 03 2000

One more term from Jud McCranie, Jun 12 2004

533043 from Jud McCranie, Oct 06 2004

a(20) = 2457639 from Jeppe Stig Nielsen, Apr 04 2020