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A370158
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a(n) is the number of prime quadruples of the form {p, p+2, p+6, p+12} with p < 10^n.
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0
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0, 1, 4, 8, 24, 76, 313, 1644, 9397, 56734, 361386, 2417777, 16785520, 120150723, 882578840
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OFFSET
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0,3
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COMMENTS
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These quadruples are adjacent twin/cousin/sexy prime pairs, and may consist of non-consecutive primes (see A086140).
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LINKS
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EXAMPLE
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The third term, the count of quad primes < 10^2, is 4 and they are: (5,7,11,17), (11,13,17,23), (17,19,23,29), (41,43,47,53). The first term, the count of quad primes <10^0, is 0 since the smallest prime is 2.
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PROG
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(Perl) use ntheory ':all'; use bigint; sub a { my $count = () = sieve_prime_cluster(1, 10**$_[0], 2, 6, 12) }; $| = 1; for (0..12) { print(a($_), ", ") } # Daniel Suteu, Feb 23 2024
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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