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).

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

1,1

Links

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

Example

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.

Maple

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

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

Crossrefs

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

Sequence in context: A217158 A214227 A337055 * A034782 A289554 A334589

Adjacent sequences: A064670 A064671 A064672 * A064674 A064675 A064676

Keyword

easy,nonn,changed

Author

Robert G. Wilson v, Oct 16 2001

Status

approved