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A125738
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Primes p such that 3^p - 3^((p + 1)/2) + 1 is prime.
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4
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3, 11, 193, 239, 659, 709, 1103, 2029, 9049, 10453, 255361, 534827, 2888387
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OFFSET
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1,1
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COMMENTS
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PrimePi[ a(n) ] = {2, 5, 44, 52, 120, 127, 185, 308, 1125, 1278 ...}, the indices of the primes p.
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LINKS
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J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
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MATHEMATICA
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Do[p=Prime[n]; f=3^p-3^((p+1)/2)+1; If[PrimeQ[f], Print[{n, p}]], {n, 1, 200}]
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CROSSREFS
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Cf. A125739 = Primes p such that 3^p + 3^((p + 1)/2) + 1 is prime.
Cf. A007670 = Numbers n such that 2^n - 2^((n + 1)/2) + 1 is prime.
Cf. A007671 = Numbers n such that 2^n + 2^((n + 1)/2) + 1 is prime.
Cf. A066408 = Numbers n such that the Eisenstein integer has prime norm.
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KEYWORD
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hard,more,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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