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A125738 Primes p such that 3^p - 3^((p + 1)/2) + 1 is prime. 4
3, 11, 193, 239, 659, 709, 1103, 2029, 9049, 10453, 255361, 534827, 2888387 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
PrimePi[ a(n) ] = {2, 5, 44, 52, 120, 127, 185, 308, 1125, 1278 ...}, the indices of the primes p.
a(14) > 4400000. - Serge Batalov, Jun 20 2023
LINKS
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.
MATHEMATICA
Do[p=Prime[n]; f=3^p-3^((p+1)/2)+1; If[PrimeQ[f], Print[{n, p}]], {n, 1, 200}]
CROSSREFS
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.
Sequence in context: A103836 A284704 A081484 * A334176 A332771 A092840
KEYWORD
hard,more,nonn
AUTHOR
Alexander Adamchuk, Dec 02 2006
EXTENSIONS
More terms from A066408 by Serge Batalov, Mar 24 2014
a(13) from Ryan Propper and Serge Batalov, Jun 20 2023
STATUS
approved

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Last modified March 29 11:44 EDT 2024. Contains 371278 sequences. (Running on oeis4.)