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A088483
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Primes p such that P = p^2 + p - 1 and P + 2 are twin primes.
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7
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2, 3, 5, 41, 59, 89, 101, 131, 743, 761, 1193, 2411, 2663, 2729, 3011, 3221, 3251, 3449, 4751, 6173, 6599, 6833, 7229, 8669, 9059, 9323, 9521, 9719, 9743, 10151, 10781, 11549, 11933, 12143, 12251, 12473, 12641, 13553, 13613, 14939, 15569, 16301
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Also primes in A155173 = Short leg A of primitive Pythagorean triangles such that perimeters are Averages of twin prime pairs... [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 21 2009]
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EXAMPLE
| a(7) = 101: 101*101 + 101 - 1 = 10301, 10301 and 10303 twin primes.
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MATHEMATICA
| lst={}; Do[p=n; q=p+1; a=q^2-p^2; c=q^2+p^2; b=2*p*q; ar=a*b/2; s=a+b+c; If[PrimeQ[s-1]&&PrimeQ[s+1], If[PrimeQ[a], AppendTo[lst, a]]], {n, 8!}]; lst ...and/or...lst={}; Do[p=Prime[n]; If[PrimeQ[p1=p*p+p-1]&&PrimeQ[p1+2], AppendTo[lst, p]], {n, 2*7!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 21 2009]
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PROG
| (PARI) forprime(p=2, 1e5, if(isprime(p^2+p-1)&&isprime(p^2+p+1), print1(p", "))) \\ Charles R Greathouse IV, Dec 27 2011
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CROSSREFS
| Cf. A088484.
Sequence in context: A128026 A041443 A057775 * A136015 A106713 A106820
Adjacent sequences: A088480 A088481 A088482 * A088484 A088485 A088486
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KEYWORD
| nonn
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AUTHOR
| Pierre CAMI (colettecami(AT)aol.com), Nov 09 2003
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