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A225431
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Primes p such that there is a prime q satisfying 3*p^2 - q^2 = 2.
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1
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OFFSET
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1,1
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COMMENTS
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Primes q: 5, 19, 71, 3691, 191861,...
(q - p)/2: 1, 4, 15, 780, 40545,...
a(7) > 2.8016852867294*10^4857. - Zak Seidov, May 09 2013
Probably finite.
This is a form of Pell's equation with the requirement that solutions be prime. - T. D. Noe, May 14 2013
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LINKS
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EXAMPLE
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11 is prime and sqrt(3*11^2 - 2) = sqrt(361) = 19 is prime, so 11 is in the sequence.
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MATHEMATICA
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nn = 1000; ta = LinearRecurrence[{4, -1}, {1, 3}, nn]; tb = LinearRecurrence[{4, -1}, {1, 5}, nn]; sol = Select[Range[nn], PrimeQ[ta[[#]]] && PrimeQ[tb[[#]]] &]; ta[[sol]] (* T. D. Noe, May 14 2013 *)
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PROG
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(PARI) v=[1, 1]; for(i=1, 1e4, v=[v[2], 4*v[2]-v[1]]; if(ispseudoprime(v[2]) && ispseudoprime(sqrtint(3*v[2]^2-2)), print1(v[2]", "))) \\ Charles R Greathouse IV, May 13 2013
(PFGW)
ABC2 Linear(3, 11, 41, 153, $a) & Linear(5, 19, 71, 265, $a)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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a(4) from R. J. Mathar, May 07 2013
a(6) from Charles R Greathouse IV, May 07 2013
a(5) from Zak Seidov, May 09 2013
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STATUS
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approved
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