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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
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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; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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
Subsequence of A051507. All terms larger than 5 are congruent to 29 mod 30. (Zak Seidov)
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EXAMPLE
| 149*151+2 = 22501. 149,151,22501 are prime so 149 is in the table.
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PROG
| (PARI) g(n, k) = forprime(x1=3, n, x2=x1+2; if(isprime(x2), p=x1*x2+k; if(isprime(p), print1(x1", ") ) ) )
(MAGMA) [p: p in PrimesUpTo(25000)| IsPrime(p+2) and IsPrime(p^2+2*p+2)] [From Vincenzo Librandi, Jan 29 2011]
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CROSSREFS
| Cf. A051779.
Sequence in context: A103993 A088269 A164371 * A087307 A038535 A090953
Adjacent sequences: A108010 A108011 A108012 * A108014 A108015 A108016
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KEYWORD
| easy,nonn
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AUTHOR
| Cino Hilliard (hillcino368(AT)gmail.com), May 30 2005
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