A007658 Numbers k such that (3^k + 1)/4 is prime. (Formerly M2420)

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, 1896463, 2533963, 2674381

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..28.

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, Generalized repunit primes, Math. Comp., 61 (1993), 927-930. [Annotated scanned copy]

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

R. G. Wilson, v, Letter to N. J. A. Sloane, circa 1991.

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

(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,more

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

a(26)=1896463 corresponds to a probable prime discovered by Paul Bourdelais, Jan 30 2020

a(27)=2533963 corresponds to a probable prime discovered by Paul Bourdelais, Mar 06 2020

a(28) from Paul Bourdelais, Mar 22 2024

Status

approved