This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A004061 M2620 #73 Apr 25 2025 04:27:24
%S A004061 3,7,11,13,47,127,149,181,619,929,3407,10949,13241,13873,16519,201359,
%T A004061 396413,1888279,3300593
%N A004061 Numbers k such that (5^k - 1)/4 is prime.
%C A004061 With the addition of the 19th prime in the sequence, the new best linear fit to the sequence has G=0.4723, which is slightly closer to the conjectured limit of G=0.56145948, A080130 (see link for Generalized Repunit Conjecture). - _Paul Bourdelais_, Apr 30 2018
%D A004061 J. Brillhart et al., Factorizations of b^n +- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 2nd edition, 1985; and later supplements.
%D A004061 Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 236.
%D A004061 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A004061 Paul Bourdelais, <a href="https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;417ab0d6.0906">A Generalized Repunit Conjecture</a> [From _Paul Bourdelais_, Jun 01 2010]
%H A004061 J. Brillhart et al., <a href="http://dx.doi.org/10.1090/conm/022">Factorizations of b^n +- 1</a>, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
%H A004061 H. Dubner, <a href="http://dx.doi.org/10.1090/S0025-5718-1993-1185243-9">Generalized repunit primes</a>, Math. Comp., 61 (1993), 927-930.
%H A004061 H. Dubner, <a href="/A028491/a028491.pdf">Generalized repunit primes</a>, Math. Comp., 61 (1993), 927-930. [Annotated scanned copy]
%H A004061 H. Lifchitz, <a href="http://www.primenumbers.net/Henri/us/MersFermus.htm">Mersenne and Fermat primes field</a>
%H A004061 S. S. Wagstaff, Jr., <a href="http://www.cerias.purdue.edu/homes/ssw/cun/index.html">The Cunningham Project</a>
%H A004061 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Repunit.html">Repunit</a>
%H A004061 <a href="/index/Pri#primepop">Index to primes in various ranges</a>, form ((k+1)^n-1)/k
%t A004061 lst={};Do[If[PrimeQ[(5^n-1)/4], AppendTo[lst, n]], {n, 10^4}];lst (* _Vladimir Joseph Stephan Orlovsky_, Aug 20 2008 *)
%o A004061 (PARI) forprime(p=2,1e4,if(ispseudoprime(5^p\4),print1(p", "))) \\ _Charles R Greathouse IV_, Jul 15 2011
%Y A004061 Cf. A080130.
%K A004061 hard,nonn,more
%O A004061 1,1
%A A004061 _N. J. A. Sloane_
%E A004061 a(13)-a(15) from Kamil Duszenko (kdusz(AT)wp.pl), Mar 25 2003
%E A004061 a(16) corresponds to a probable prime based on trial factoring to 4*10^13 and Fermat primality testing base 2. - _Paul Bourdelais_, Dec 11 2008
%E A004061 a(17) corresponds to a probable prime discovered by _Paul Bourdelais_, Jun 01 2010
%E A004061 a(18) corresponds to a probable prime discovered by _Paul Bourdelais_, Apr 30 2018
%E A004061 a(19) corresponds to a probable prime discovered by _Ryan Propper_, Jan 02 2022