OFFSET
1,1
COMMENTS
Corresponding primes (q^p-1)/(q-1) are listed in A123488.
From Robert G. Wilson v, Dec 28 2016: (Start)
Conjecture: Never is a(n) equal to 0.
Records: 2, 5, 113, 151, 307, 491, 2003, 6389, 7883, 11813, 18587, 31721, 40763, ... ;
First occurrence of the k_th prime: 1, 20, 5, 32, 21, 33, 81, 17, ... ;
Positions where two occurs: 1, 2, 3, 4, 6, 7, 8, 11, 18, 24, 28, 31, 98, 111, ... ;
Positions where three occurs: 20, 27, 100, 182, ... ;
Positions where five occurs: 5, 15, 35, 42, 114, 158, ... ; etc. (End)
Jones & Zvonkin conjecture (as did Robert G. Wilson v above) that a(n) > 0 for all n. - Charles R Greathouse IV, Jul 23 2021
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..205
Gareth A. Jones and Alexander K. Zvonkin, Groups of prime degree and the Bateman-Horn Conjecture, arXiv:2106.00346 [math.GR], 2021.
MATHEMATICA
f[n_] := NestWhile[NextPrime, 2, ! PrimeQ[Cyclotomic[Prime[n], #]] &]; Array[f, 63](* Davin Park, Dec 28 2016 and Robert G. Wilson v, Dec 28 2016 *)
PROG
(PARI) a(n) = {my(x = 2); while (!isprime(polcyclo(prime(n), x)), x= nextprime(x+1)); x; } \\ Michel Marcus, Dec 10 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, Sep 30 2006, Oct 02 2006
STATUS
approved