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

Author

Peter Luschny, Dec 25 2008

Keywords

• nonn

Examples

			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.
		

Links

• Jean-François Alcover, Table of n, a(n) for n = 1..100
• P. Luschny, Von Staudt prime number, definition and computation.

Crossrefs

Cf. A092307, A005385 and A152951.

Programs

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 *)