A245237 Numbers k such that (48^k - 1)/47 is prime.

19, 269, 349, 383, 1303, 15031, 200443, 343901

Offset: 1

Author

Robert Price, Jul 14 2014

Keywords

• hard
• more
• nonn

Comments

a(7) > 10^5.

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, A242797, A243279.

Programs

Maple

A245237:=n->`if`(isprime((48^n - 1)/47), n, NULL); seq(A245237(n), n=1..100000); # Wesley Ivan Hurt, Apr 12 2014

Mathematica

Select[Prime[Range[100000]], PrimeQ[(48^# - 1)/47] &]

PARI

is(n)=ispseudoprime((48^n-1)/47) \\ Charles R Greathouse IV, Jun 06 2017

Extensions

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

a(8) from Paul Bourdelais, Mar 03 2025