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A152951
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Complementary von Staudt prime numbers.
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3
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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
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OFFSET
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0,1
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COMMENTS
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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.
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LINKS
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MAPLE
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select(j->(denom(bernoulli(j-1)/(j-1))<>12*j), select(isprime, [seq(12*k-1, k=1..100)]));
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MATHEMATICA
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Select[ 12*Range[200] - 1, PrimeQ[#] && 12 # != Denominator[ BernoulliB[# - 1]/(# - 1)]& ] ] (* Jean-François Alcover, Jul 29 2013 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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