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A004061 Numbers n such that (5^n - 1)/4 is prime.
(Formerly M2620)
51
3, 7, 11, 13, 47, 127, 149, 181, 619, 929, 3407, 10949, 13241, 13873, 16519, 201359, 396413 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

With the addition of the 17th prime in the sequence, the new best linear fit to the sequence has G=0.44676, which is slightly closer to the conjectured limit of G=0.56145948 (see link for Generalized Repunit Conjecture). [Paul Bourdelais, Jun 01 2010]

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..17.

Paul Bourdelais,A Generalized Repunit Conjecture [From Paul Bourdelais, Jun 01 2010]

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.

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[(5^n-1)/4], AppendTo[lst, n]], {n, 10^4}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 20 2008 *)

PROG

(Other) PFGW v3.3.1 [Paul Bourdelais, Jun 01 2010]

(PARI) forprime(p=2, 1e4, if(ispseudoprime(5^p\4), print1(p", "))) \\ Charles R Greathouse IV, Jul 15 2011

CROSSREFS

Sequence in context: A059055 A243367 A145670 * A000572 A059568 A003512

Adjacent sequences:  A004058 A004059 A004060 * A004062 A004063 A004064

KEYWORD

hard,nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

3 more terms from Kamil Duszenko (kdusz(AT)wp.pl), Mar 25 2003

a(16)=201359 is a probable prime based on trial factoring to 4*10^13 and Fermat primality testing base 2. - Paul Bourdelais, Dec 11 2008

a(17)=396413 is a probable prime discovered by Paul Bourdelais, Jun 01 2010

STATUS

approved

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Last modified December 22 16:00 EST 2014. Contains 252364 sequences.