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

Offset

0,1

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

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

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 *)

Prog

(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

Crossrefs

Cf. A092307.

Sequence in context: A244167 A115395 A142647 * A090799 A044194 A044575

Adjacent sequences: A152948 A152949 A152950 * A152952 A152953 A152954

Keyword

easy,nonn

Author

Peter Luschny, Dec 24 2008

Status

approved