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A084865
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Primes of the form 2x^2 + 3y^2.
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6
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2, 3, 5, 11, 29, 53, 59, 83, 101, 107, 131, 149, 173, 179, 197, 227, 251, 269, 293, 317, 347, 389, 419, 443, 461, 467, 491, 509, 557, 563, 587, 653, 659, 677, 683, 701, 773, 797, 821, 827, 941, 947, 971, 1013, 1019, 1061, 1091, 1109, 1163, 1181, 1187
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OFFSET
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1,1
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COMMENTS
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Is it true that a(n) = A019338(n+1)?
Comment: The truth of the conjecture A084863(a(n))=1 follows from the genus theory of quadratic forms (see Cox, page 61). By comparing enough terms, we see that the conjecture a(n) = A019338(n+1) is false. - T. D. Noe, May 02 2008
Appears to be the primes p such that (p mod 6)*(Fibonacci(p) mod 6)=25. - Gary Detlefs, May 26 2014
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REFERENCES
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David A. Cox, Primes of the Form x^2 + n y^2, Wiley, 1989.
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LINKS
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FORMULA
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The primes are congruent to {2, 3, 5, 11} (mod 24). - T. D. Noe, May 02 2008
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EXAMPLE
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A000040(17) = 59 = 32 + 27 = 2*4^2 + 3*3^2, therefore 59 is a term.
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MATHEMATICA
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QuadPrimes2[2, 0, 3, 10000] (* see A106856 *)
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PROG
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(PARI) list(lim)=my(v=List(), w, t); for(x=0, sqrtint(lim\2), w=2*x^2; for(y=0, sqrtint((lim-w)\3), if(isprime(t=w+3*y^2), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Feb 09 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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