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A007658 Numbers n such that (3^n + 1)/4 is prime.
(Formerly M2420)
28
3, 5, 7, 13, 23, 43, 281, 359, 487, 577, 1579, 1663, 1741, 3191, 9209, 11257, 12743, 13093, 17027, 26633, 104243, 134227, 152287, 700897, 1205459 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Prime repunits in base -3.

REFERENCES

J. Brillhart et al., Factorizations of b^n +- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 2nd edition, 1985; and later supplements.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=1..25.

P. Bourdelais,A Generalized Repunit Conjecture

J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.

H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.

H. Lifchitz, Mersenne and Fermat primes field

S. S. Wagstaff, Jr., The Cunningham Project

Eric Weisstein's World of Mathematics, Repunit

MATHEMATICA

lst={}; Do[If[PrimeQ[(3^n+1)/4], Print[n]; AppendTo[lst, n]], {n, 10^5}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 21 2008 *)

PROG

(Other) PFGW v3.3.1 - Paul Bourdelais, Apr 05 2010

(PARI) is(n)=ispseudoprime((3^n+1)/4) \\ Charles R Greathouse IV, Apr 29 2015

CROSSREFS

Sequence in context: A077949 A077974 A126273 * A275175 A267549 A154321

Adjacent sequences:  A007655 A007656 A007657 * A007659 A007660 A007661

KEYWORD

hard,nonn

AUTHOR

N. J. A. Sloane, Robert G. Wilson v

EXTENSIONS

a(20) from Robert G. Wilson v, Apr 11 2005

a(22)=134227 corresponds to a probable prime discovered by Paul Bourdelais, Nov 08 2007

a(23)=152287 corresponds to a probable prime discovered by Paul Bourdelais, Apr 07 2008

a(24)=700897 corresponds to a probable prime discovered by Paul Bourdelais, Apr 05 2010

a(25)=1205459 corresponds to a probable prime discovered by Paul Bourdelais, Aug 28 2015

STATUS

approved

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Last modified June 26 16:32 EDT 2017. Contains 288766 sequences.