login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A123487 Smallest prime q such that (q^p-1)/(q-1) is prime, where p = prime(n); or 0 if no such prime q exists. 7
2, 2, 2, 2, 5, 2, 2, 2, 113, 151, 2, 61, 53, 89, 5, 307, 19, 2, 491, 3, 11, 271, 41, 2, 271, 359, 3, 2, 79, 233, 2, 7, 13, 11, 5, 29, 71, 139, 127, 139, 2003, 5, 743, 673, 593, 383, 653, 661, 251, 6389, 2833, 223, 163, 37, 709, 131, 41, 2203, 941, 2707, 13, 1283, 383 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Corresponding primes (q^p-1)/(q-1) are listed in A123488.

a(n) coincides with A066180(n) when A066180(n) is prime or 0.

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)

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..205

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

Cf. A123488, A066180, A084732.

Sequence in context: A130086 A084731 A066180 * A130325 A154097 A221491

Adjacent sequences:  A123484 A123485 A123486 * A123488 A123489 A123490

KEYWORD

nonn

AUTHOR

Alexander Adamchuk, Sep 30 2006, Oct 02 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 5 15:37 EDT 2020. Contains 334852 sequences. (Running on oeis4.)