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Search: id:A108016
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| A108016 |
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Primes of the form p(p+2)+6 where p and p+2 are primes. |
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1
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| 41, 149, 5189, 39209, 186629, 213449, 1127849, 1192469, 1695209, 2965289, 3732629, 4359749, 4460549, 5673929, 6718469, 7225349, 11370389, 12446789, 12830729, 14607689, 14837909, 16016009, 17040389, 17288969, 20684309
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Except for the first term, these numbers end in 9. p can take one of the forms 10k+1,10k+3,10k+7 or 10k+9. p=10k+1 => p(p+2)+6 = (10k+1)(10k+3)+6 = 10h+9. p can be 10k+1. p=10k+3 => p+2 = 0 mod 5 not prime. p cannot be 10k+3. p=10k+7 => p(p+2)+6 = (10k+7)(10k+9)+6 = 10h+9. p can be 10k+7. p=10k+9 => p(p+2)+6 = (10k+9)*(10k+11)+6 = 0 mod 5 not prime. p cannot be 10k+9. Thus by exhaustion p(p+2)+6 ends in 9.
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EXAMPLE
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11*13 + 6 = 149.
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PROGRAM
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(PARI) g(n, k) = forprime(x1=3, n, x2=x1+2; if(isprime(x2), p=x1*x2+k; if(isprime(p), print1(x1", ") ) ) )
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CROSSREFS
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Cf. A051779.
Adjacent sequences: A108013 A108014 A108015 this_sequence A108017 A108018 A108019
Sequence in context: A044754 A050954 A141957 this_sequence A142630 A082252 A105100
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), May 31 2005
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