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

Author

Robert G. Wilson v, Oct 16 2001

Keywords

• easy
• nonn

Examples

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

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.

Crossrefs

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

Programs

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 *)

PARI

a(n) = {forprime(p=2, , forprime(q=2, p-1, if ((p-1)/(q-1) == n, return (p));););} \\ Michel Marcus, Apr 16 2016

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

Extensions

Definition corrected by Stephanie Anderson, Apr 16 2016