A057025 Smallest prime of form (2n+1)*2^m+1 for some m.

2, 7, 11, 29, 19, 23, 53, 31, 137, 1217, 43, 47, 101, 109, 59, 7937, 67, 71, 149, 79, 83, 173, 181

Offset: 0

Author

Henry Bottomley, Jul 24 2000

Keywords

• nonn

Comments

next term a(23) = 47*2^583+1 > 10^177. Sequence then continues: 197, 103, 107, 881, 229, 1889, 977, 127, 131, 269, 139, 569, 293, 151, 617, 317, 163, 167, 1361, 349, 179, 23297, 373, 191, 389, 199, 809, ...

If no such prime exists for any m then 2n+1 is called a Sierpiński number. One could use a(n) = 0 for these cases. E.g., a(39278) = 0 because 78557 is a Sierpiński number. For the corresponding numbers m see A046067(n+1), n >= 0, where -1 entries corresponds to a(n) = 0. See also the Sierpiński links there. - Wolfdieter Lang, Feb 07 2013

Examples

			a(5)=23 because 2*5+1=11 and smallest prime of the form 11*2^m+1 is 23 (since 11+1=12 is not prime)
		

Links

• Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime

Crossrefs

Cf. A032373, A057023, A057026, A046067.