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A152951 Complementary von Staudt prime numbers. 3
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified March 28 22:27 EDT 2017. Contains 284249 sequences.