1,1

Using a sieve, these primes can be generated quickly. In the set of primes < 10^9, the density of these primes is about 1/10. It is easy to show that this sequence contains all "safe" primes (A005385).

Primes p such that 6p is the denominator of some Bernoulli number. - T. D. Noe, Sep 26 2006

Except for 5 and 7, primes p such that 12p is the denominator of B(p-1)/(p-1) where B(n) is the Bernoulli number. [From Peter Luschny (peter(AT)luschny.de), Dec 24 2008]

T. D. Noe, Table of n, a(n) for n=1..1000

P. Luschny, Von Staudt prime number, definiton and computation. [From Peter Luschny (peter(AT)luschny.de), Dec 24 2008]

Let h(x)=12x(x+ln(exp(-x)-1)-ln(x)) and [x^n]S(h) denote the coefficient of x^n in the series expansion of h. Consider for n>1 the relation n = denominator((n-1)![x^n]S(h)). [From Peter Luschny (peter(AT)luschny.de), Dec 24 2008]

For p>7: seq(`if`(denom(bernoulli(n-1)/(n-1))=12*n, n, NULL), n=2..500); [From Peter Luschny (peter(AT)luschny.de), Dec 24 2008]

t=Table[p=Prime[n]; Length[Select[Divisors[p-1]+1, PrimeQ], {n, 150}]; Prime[Flatten[Position[t, 3]]]

Cf. A090801 (distinct numbers appearing as denominators of Bernoulli numbers)

Cf. A092308 (for p=prime(n), the number of primes q such that q-1 divides p-1).

Cf. A005385 (primes p such that (p-1)/2 is also prime).

Cf. A152951. [From Peter Luschny (peter(AT)luschny.de), Dec 24 2008]

Sequence in context: A124111 A151715 A090810 this_sequence A005385 A075705 A141305

Adjacent sequences: A092304 A092305 A092306 this_sequence A092308 A092309 A092310

nonn

T. D. Noe (noe(AT)sspectra.com), Feb 12 2004