A242797 Numbers n such that (45^n - 1)/44 is prime.

19, 53, 167, 3319, 11257, 34351, 216551

Offset: 1

Author

Robert Price, May 22 2014

Keywords

• hard
• more
• nonn

Comments

a(7) > 10^5.

Numbers corresponding to a(4)-a(6) are probable primes.

All terms are prime.

Links

• Harvey Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927-930.
• Henri Lifchitz, Mersenne and Fermat primes field

Crossrefs

Cf. A028491, A004061, A004062, A004063, A004023, A005808, A004064, A016054, A006032, A006033, A006034, A006035, A127995, A127996, A127997, A127998, A127999, A098438, A128002, A128003, A128004, A128005, A240765.

Programs

Maple

A242797:=n->`if`(isprime((45^n - 1)/44), n, NULL); seq(A242797(n), n=1..100000); # Wesley Ivan Hurt, Apr 12 2014

Mathematica

Select[Prime[Range[100000]], PrimeQ[(45^# - 1)/44] &]

PARI

is(n)=ispseudoprime((45^n-1)/44) \\ Charles R Greathouse IV, Feb 20 2017

Extensions

a(7)=216551 corresponds to a probable prime discovered by Paul Bourdelais, Aug 04 2020