

A004061


Numbers n such that (5^n  1)/4 is prime.
(Formerly M2620)


38



3, 7, 11, 13, 47, 127, 149, 181, 619, 929, 3407, 10949, 13241, 13873, 16519, 201359, 396413, 1888279
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OFFSET

1,1


COMMENTS

With the addition of the 18th prime in the sequence, the new best linear fit to the sequence has G=0.46271, which is slightly closer to the conjectured limit of G=0.56145948 (see link for Generalized Repunit Conjecture). [Paul Bourdelais, Apr 30 2018]


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..18.
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), 927930.
H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927930. [Annotated scanned copy]
H. Lifchitz, Mersenne and Fermat primes field
S. S. Wagstaff, Jr., The Cunningham Project
Eric Weisstein's World of Mathematics, Repunit
Index to primes in various ranges, form ((k+1)^n1)/k


MATHEMATICA

lst={}; Do[If[PrimeQ[(5^n1)/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 * A277009 A277019 A310201
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
a(18)=1888279 is a probable prime discovered by Paul Bourdelais, Apr 30 2018


STATUS

approved



