A064652 -id:A064652 - cp's OEIS frontend

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

Robert G. Wilson v, Oct 16 2001

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

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.

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

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 *)

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

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

Definition corrected by Stephanie Anderson, Apr 16 2016

A064673 Where the least prime p such that n = (p-1)/(q-1) and p > q is not the least prime == 1 (mod n) (A034694).

Original entry on oeis.org

24, 32, 34, 38, 62, 64, 71, 76, 80, 92, 94, 104, 110, 117, 122, 124, 129, 132, 144, 149, 152, 154, 159, 164, 167, 182, 184, 185, 188, 201, 202, 206, 212, 214, 218, 220, 225, 227, 236, 242, 244, 246, 252, 264, 269, 272, 274, 286, 290, 294

Offset: 1

Robert G. Wilson v, Oct 16 2001

			24 is in the sequence because (97-1)/(5-1) whereas the first prime ==1 (Mod 24) is 73. See the comment in A034694 about the multiplier k and it must differ from q-1 or k+1 is not prime.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A034694, A064632, A064652. Disjoint from A005097 and A006093.

f:= proc(n) local k;
  for k from n+1 by n do
    if isprime(k) then return k fi
  od
end proc:
filter:= proc(n) local p;
    p:= f(n);
    not isprime(1+(p-1)/n)
end proc:
select(filter, [$1..1000]); # Robert Israel, May 09 2024

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]]; k = 1; While[ !PrimeQ[k*n + 1], k++ ]; If[p != k*n + 1, Print[n]], {n, 2, 300} ]

cp's OEIS Frontend

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

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Sage

Extensions