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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).
3
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
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
KEYWORD
easy,nonn
AUTHOR
Robert G. Wilson v, Oct 16 2001
STATUS
approved