A006034 -id:A006034 - cp's OEIS frontend

A185073 Numbers n such that (34^n - 1)/33 is prime.

13, 1493, 5851, 6379, 125101

Offset: 1

Robert Price, Mar 10 2012

H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927-930.
H. Lifchitz, Mersenne and Fermat primes field
P. Bourdelais, A Generalized Repunit Conjecture

Cf. A028491, A004061, A004062, A004063, A004064, A004023, A005808, A016054, A006032, A006033, A006034, A006035, A098438, A127995-A128005.

Select[Prime[Range[100]], PrimeQ[(34^#-1)/33]&]

isok(n) = isprime((34^n-1)/33); \\ Michel Marcus, Mar 13 2016

lista(nn) = for(n=1, nn, if(ispseudoprime((34^n - 1)/33), print1(n, ", "))); \\ Altug Alkan, Mar 13 2016

a(5)=125101 corresponds to a probable prime discovered by Paul Bourdelais, Nov 20 2017

A294722 Numbers k such that (44^k - 1)/43 is prime.

Original entry on oeis.org

5, 31, 167, 100511

Offset: 1

Paul Bourdelais, Nov 07 2017

The number corresponding to a(4) is a probable prime.

These are the indices of base-44 repunit primes, i.e., numbers k such that A002275(k) interpreted as a base-44 number and converted to decimal is prime. - Felix Fröhlich, Nov 08 2017

P. Bourdelais, A generalized repunit conjecture

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

ParallelMap[ If[ PrimeQ[(44^# - 1)/43], #, Nothing] &, Prime@Range @ 10000] (* Robert G. Wilson v, Nov 25 2017 *)

is(n) = ispseudoprime((44^n-1)/43) \\ Felix Fröhlich, Nov 08 2017

ABC2 (44^$a-1)/43 // -f{2*$a}
a: primes from 2 to 1000000

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A185073 Numbers n such that (34^n - 1)/33 is prime.

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A294722 Numbers k such that (44^k - 1)/43 is prime.

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