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Search: id:A108013
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| A108013 |
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Primes p such that p+2 and p(p+2)+2 are primes. |
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+0
1
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| 3, 5, 149, 179, 239, 269, 419, 569, 1289, 1319, 2309, 2549, 2729, 3359, 3389, 4259, 4649, 5849, 5879, 6359, 6779, 8999, 9239, 9629, 10529, 10889, 11969, 13679, 13829, 14009, 14549, 16229, 16649, 18059, 18119, 18539, 19139, 19379, 21599, 21839
(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 2 terms, these numbers all end in 9. Froof: Any odd prime P>5 can have one of the following forms: 10k+1,10k+3,10k+7,10k+9. 10k+1 => p(p+2)+2 ends in 5 not prime so p <> form 10k+1 10k+3 => (p+2) ends in 5 not prime so p <> form 10k+3 10k+7 => p(p+2)+2 ends in 5 not prime so p <> form 10k+7 Thus p is of the form 10k+9 as stated. Moreover, p+2 ends in 1 and p(p+2)+2 is of the form 100h+1 since (10k+9)(10k+11)+2 = 100(k^2+2k+1)+1
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EXAMPLE
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149*151+2 = 22501. 149,151,22501 are prime so 149 is in the table.
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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.
Sequence in context: A070743 A103993 A088269 this_sequence A087307 A038535 A090953
Adjacent sequences: A108010 A108011 A108012 this_sequence A108014 A108015 A108016
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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 30 2005
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