A152952 Von Staudt primes which are not safe primes (A005385).

239, 443, 647, 659, 827, 1223, 1259, 1499, 1787, 1847, 2087, 2243, 2339, 2687, 2699, 3299, 3659, 3767, 4943, 5903, 6263, 6287, 6299, 6563, 6863, 6959, 7043, 7487, 7583, 7883, 7907, 7919, 8087, 8219, 8243, 8387, 8627, 8663

Offset

1,1

Links

Jean-François Alcover, Table of n, a(n) for n = 1..100

P. Luschny, Von Staudt prime number, definition and computation.

Example

239 is a von Staudt prime because the denominator(B(239-1)/(239-1))=239*12, where B(n) is the Bernoulli number, but (239-1)/2=119=7*17 is not a prime.

Maple

a := proc(n) local k, L; L:= []; for k from 11 by 12 to n do map(i->i+1, divisors(k-1)); select(isprime, %) minus {2, 3}; if % = {k} then L := [op(L), k] fi; od; select(isprime, map(i->i+i+1, select(isprime, [$1..iquo(n, 2)]))): sort(convert(convert(L, set) minus convert(%, set), list)): end:

Mathematica

vonStaudtPrimeQ[p_?PrimeQ] := Denominator[BernoulliB[p-1]/(p-1)] == 12*p; safePrimeQ[p_?PrimeQ] := PrimeQ[(p-1)/2]; Reap[For[p = 2, p < 10^4, p = NextPrime[p], If[vonStaudtPrimeQ[p] && !safePrimeQ[p], Print[p]; Sow[p]]]][[2, 1]] (* Jean-François Alcover, Jan 27 2014 *)

Crossrefs

Cf. A092307, A005385 and A152951.

Sequence in context: A294092 A056086 A046012 * A142356 A142557 A164290

Adjacent sequences: A152949 A152950 A152951 * A152953 A152954 A152955

Keyword

nonn

Author

Peter Luschny, Dec 25 2008

Status

approved