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A057171 Numbers n such that (5^n+1)/6 is a prime. 34


%S 5,67,101,103,229,347,4013,23297,30133,177337,193939,266863,277183,

%T 335429,1856147

%N Numbers n such that (5^n+1)/6 is a prime.

%C With the discovery of a(15), the best fit line slope G=0.55167 (see link to Generalized Repunit Conjecture). This sequence is converging nicely to the conjectured slope G=0.56145948. - _Paul Bourdelais_, Feb 26 2019

%H Paul Bourdelais, <a href="https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;417ab0d6.0906">A Generalized Repunit Conjecture</a>

%H 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 H. Dubner and T. Granlund, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL3/DUBNER/dubner.html">Primes of the Form (b^n+1)/(b+1)</a>, J. Integer Sequences, 3 (2000), #P00.2.7.

%H H. Lifchitz, <a href="http://www.primenumbers.net/Henri/us/MersFermus.htm">Mersenne and Fermat primes field</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Repunit.html">Repunit</a>

%H R. G. Wilson, v, <a href="/A084740/a084740.pdf">Letter to N. J. A. Sloane, circa 1991.</a>

%t a={};Do[x=(5^n+1)/6;If[PrimeQ[x],AppendTo[a,n]],{n,0,12^2}];a (* _Vladimir Joseph Stephan Orlovsky_, Apr 29 2008 *)

%o (PARI) isok(n) = (denominator(p=(5^n+1)/6) == 1) && isprime(p); \\ _Michel Marcus_, Oct 28 2017

%K nonn,more

%O 1,1

%A _N. J. A. Sloane_, Sep 15 2000

%E More terms from Kamil Duszenko (kdusz(AT)wp.pl), Jun 23 2003

%E 30133 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 05 2008

%E a(10) discovered 10/29/08 is a probable prime based on trial factoring to 3.5e13 and Fermat testing base 2. - _Paul Bourdelais_, Nov 04 2008

%E a(11)=193939 from Paul Bourdelais discovered 12/24/08 is a probable prime based on trial factoring to 4e13 and Fermat primality testing base 2. - _Paul Bourdelais_, Dec 24 2008

%E a(12)=266863 is a probable prime discovered by _Paul Bourdelais_, Jul 09 2010

%E a(13)=277183 is a probable prime discovered by _Paul Bourdelais_, Jul 16 2010

%E a(14)=335429 is a probable prime discovered by _Paul Bourdelais_, Aug 23 2010

%E a(15)=1856147 corresponds to a probable prime discovered by _Paul Bourdelais_, Feb 26 2019

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Last modified June 18 07:06 EDT 2019. Contains 324203 sequences. (Running on oeis4.)