A032373 -id:A032373 - cp's OEIS frontend

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

Henry Bottomley, Jul 24 2000

nonn

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

			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)

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

Cf. A032373, A057023, A057026, A046067.

A032419 Numbers k such that 139*2^k + 1 is prime.

Original entry on oeis.org

2, 14, 914, 12614, 335522, 1567874

Offset: 1

James R. Buddenhagen

Ray Ballinger, Proth Search Page
Ray Ballinger & Wilfrid Keller, List of primes k.2^n + 1 for k < 300.
Y. Gallot, Proth.exe: Windows Program for Finding Large Primes
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 prime

Cf. A032418, A032373, A032420, A032460, A032497.

select(k->isprime(139*2^k+1),[$0..1000])[]; # Muniru A Asiru, Dec 18 2018

Select[Range[1000], PrimeQ[139*2^# + 1] & ] (* Robert Price, Dec 18 2018 *)

is(n)=ispseudoprime(139*2^n+1) \\ Charles R Greathouse IV, Jun 07 2017

One more term (from the Ballinger-Keller web page) from M. F. Hasler, Apr 18 2007

a(6) from the Ray Ballinger and Wilfrid Keller link by Robert Price, Dec 18 2018

A032497 Numbers n such that 241*2^n+1 is prime.

Original entry on oeis.org

36, 72, 288, 5528, 8904, 9876, 130992

Offset: 1

N. J. A. Sloane

Ray Ballinger, Proth Search Page
Ray Ballinger & 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 prime

Cf. A032373, A032419, A032460.

is(n)=ispseudoprime(241*2^n+1) \\ Charles R Greathouse IV, Jun 07 2017

One more term (from the Ballinger-Keller web page) from M. F. Hasler, Apr 18 2007

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

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A032419 Numbers k such that 139*2^k + 1 is prime.

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A032497 Numbers n such that 241*2^n+1 is prime.

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