This site is supported by donations to The OEIS Foundation.



Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A004061 Numbers n such that (5^n - 1)/4 is prime.
(Formerly M2620)
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)



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]


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).


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

Index to primes in various ranges, form ((k+1)^n-1)/k


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


(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


Sequence in context: A059055 A243367 A145670 * A277009 A277019 A260484

Adjacent sequences:  A004058 A004059 A004060 * A004062 A004063 A004064




N. J. A. Sloane.


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



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 8 01:14 EST 2016. Contains 278902 sequences.