A064632 Smallest prime p such that n = (p-1)/(q-1) for some prime q.

3, 7, 5, 11, 7, 29, 17, 19, 11, 23, 13, 53, 29, 31, 17, 103, 19, 191, 41, 43, 23, 47, 97, 101, 53, 109, 29, 59, 31, 311, 193, 67, 137, 71, 37, 149, 229, 79, 41, 83, 43, 173, 89, 181, 47, 283, 97, 197, 101, 103, 53, 107, 109, 331, 113, 229, 59, 709, 61, 367, 373

Offset

2,1

Links

Daria Micovic, Table of n, a(n) for n = 2..10000

Matthew M. Conroy, A sequence related to a conjecture of Schinzel, , J. Integ. Seqs. Vol. 4 (2001), #01.1.7.

Example

a(7) = 29 because (29-1)/(5-1).

Mathematica

NextPrim[n_] := (k = n + 1; While[ !PrimeQ[k], k++ ]; k); Do[p = 2; While[q = (p - 1)/n + 1; !PrimeQ[q] || q >= p, p = NextPrim[p]]; Print[p], {n, 2, 100} ]
spp[n_]:=Module[{p=2}, While[!PrimeQ[(p-1)/n+1], p=NextPrime[p]]; p]; Array[ spp, 70, 2] (* Harvey P. Dale, Aug 22 2019 *)

Prog

(Sage)
def A064632(n):
    p, q = 0, 0
    while not (q.is_prime() and q < p):
        p = next_prime(p)
        if p % n != 1: continue
        q = (p - 1) // n + 1
    return p # Daria Micovic, Apr 13 2016
(PARI) a(n) = {forprime(p=2, , forprime(q=2, p-1, if ((p-1)/(q-1) == n, return (p)); ); ); } \\ Michel Marcus, Apr 16 2016

Crossrefs

Similar to but not the same as A034694. Cf. A064652 (q-values), A064673.

Sequence in context: A254929 A066677 A061026 * A216487 A328984 A328190

Adjacent sequences: A064629 A064630 A064631 * A064633 A064634 A064635

Keyword

easy,nonn

Author

Robert G. Wilson v, Oct 16 2001

Extensions

Definition corrected by Stephanie Anderson, Apr 16 2016

Status

approved