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Search: id:A125739
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| A125739 |
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Primes p such that 3^p + 3^((p + 1)/2) + 1 is prime. |
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+0
4
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| 3, 5, 7, 17, 19, 79, 163, 317, 353, 1049, 1759, 5153, 7541, 23743
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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PrimePi[ a(n) ] = {2, 3, 4, 7, 8, 22, 38, 66, 71, 176, ...}.
No other terms up to 17000. - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Sep 08 2007
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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.
S. S. Wagstaff, Jr., The Cunningham Project.
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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. A125738 = 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.
Sequence in context: A001259 A087126 A062547 this_sequence A122853 A137258 A053341
Adjacent sequences: A125736 A125737 A125738 this_sequence A125740 A125741 A125742
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KEYWORD
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hard,more,nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Dec 02 2006
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EXTENSIONS
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a(11)-a(13) from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Sep 08 2007
a(14) from Lelio R Paula (lelio(AT)sknet.com.br), May 07 2008
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