A152951 Complementary von Staudt prime numbers.

71, 131, 191, 251, 311, 419, 431, 491, 599, 683, 743, 911, 947, 971, 1031, 1091, 1103, 1151, 1163, 1427, 1451, 1511, 1559, 1571, 1583, 1607, 1667, 1811, 1871, 1931, 1979, 2003, 2111, 2267, 2351, 2399, 2411, 2423, 2531, 2543, 2591, 2663, 2711, 2843, 2927, 2939

Offset: 0

Author

Peter Luschny, Dec 24 2008

Keywords

• easy
• nonn

Comments

A prime number in the arithmetic progression 12n-1 which is not a von Staudt prime number, i.e., 12p <> denominator(B(p-1)/(p-1)), where B(n) is the Bernoulli number.

Links

• Dana Jacobsen, Table of n, a(n) for n = 0..10883
• Peter Luschny, Von Staudt prime number, definition and computation.

Crossrefs

Cf. A092307.

Programs

Maple

select(j->(denom(bernoulli(j-1)/(j-1))<>12*j),select(isprime,[seq(12*k-1,k=1..100)]));

Mathematica

Select[ 12*Range[200] - 1, PrimeQ[#] && 12 # != Denominator[ BernoulliB[# - 1]/(# - 1)]& ] (* Jean-François Alcover, Jul 29 2013 *)

Perl

use ntheory ":all"; forprimes { my $p=$; say if $ % 12 == 11 && vecany { $ > 3 && $ < $p-1 && is_prime($+1) } divisors($p-1); } 10000; # _Dana Jacobsen, Dec 29 2015

Perl

use ntheory ":all"; forprimes { say if $ % 12 == 11 && (bernfrac($-1))[1] != 6*$; } 10000; # _Dana Jacobsen, Dec 29 2015

Extensions

More terms from Dana Jacobsen, Dec 29 2015