A007658 Numbers k such that (3^k + 1)/4 is prime.
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, 7034611
Offset: 1
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
- Paul 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
- Robert G. Wilson v, Letter to N. J. A. Sloane, circa 1991.
Programs
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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 *) -
PARI
is(n)=ispseudoprime((3^n+1)/4) \\ Charles R Greathouse IV, Apr 29 2015
Extensions
a(20) from Robert G. Wilson v, Apr 11 2005
a(22) from Paul Bourdelais, Nov 08 2007
a(23) from Paul Bourdelais, Apr 07 2008
a(24) from Paul Bourdelais, Apr 05 2010
a(25) from Paul Bourdelais, Aug 28 2015
a(26) from Paul Bourdelais, Jan 30 2020
a(27) from Paul Bourdelais, Mar 06 2020
a(28) from Paul Bourdelais, Mar 22 2024
a(29) from Paul Bourdelais, Dec 04 2024
Comments