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%I #15 Jan 28 2019 23:51:24
%S 71,131,191,251,311,419,431,491,599,683,743,911,947,971,1031,1091,
%T 1103,1151,1163,1427,1451,1511,1559,1571,1583
%N Complementary von Staudt prime numbers.
%C 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.
%H Dana Jacobsen, <a href="/A152951/b152951.txt">Table of n, a(n) for n = 0..10883</a>
%H P. Luschny, <a href="http://www.luschny.de/math/zeta/VonStaudtPrimes.html">Von Staudt prime number, definition and computation.</a>
%p select(j->(denom(bernoulli(j-1)/(j-1))<>12*j),select(isprime,[seq(12*k-1,k=1..100)]));
%t Select[ 12*Range[200] - 1, PrimeQ[#] && 12 # != Denominator[ BernoulliB[# - 1]/(# - 1)]& ] ] (* _Jean-François Alcover_, Jul 29 2013 *)
%o (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
%o (Perl) use ntheory ":all"; forprimes { say if $_ % 12 == 11 && (bernfrac($_-1))[1] != 6*$_; } 10000; # _Dana Jacobsen_, Dec 29 2015
%Y Cf. A092307.
%K easy,nonn
%O 0,1
%A _Peter Luschny_, Dec 24 2008
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