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A057171
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Numbers n such that (5^n+1)/6 is a prime.
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20
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5, 67, 101, 103, 229, 347, 4013, 23297, 30133, 177337, 193939, 266863, 277183, 335429
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| With the discovery of a(13), the best fit line slope G=0.59823 (see link to Generalized Repunit Conjecture). This sequence is converging nicely to the conjectured slope G=0.56145948. [From Paul Bourdelais (pbourdelais(AT)radiantblue.com), Jul 16 2010]
With the discovery of a(14), the best fit line slope G=0.56243 (see link to Generalized Repunit Conjecture). This sequence is converging nicely to the conjectured slope G=0.56145948. [From Paul Bourdelais (pbourdelais(AT)radiantblue.com), Aug 23 2010]
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LINKS
| J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.
Eric Weisstein's World of Mathematics, Repunit
H. Lifchitz, Mersenne and Fermat primes field
Paul Bourdelais,A Generalized Repunit Conjecture [From Paul Bourdelais (pbourdelais(AT)radiantblue.com), Jul 09 2010]
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MAPLE
| MATLAB [From Paul Bourdelais (paul.bourdelais(AT)gd-ais.com), Dec 24 2008]
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MATHEMATICA
| a={}; Do[x=(5^n+1)/6; If[PrimeQ[x], AppendTo[a, n]], {n, 0, 12^2}]; a - Vladimir Orlovsky (4vladimir(AT)gmail.com), Apr 29 2008
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PROG
| (Other) MATLAB [From Paul Bourdelais (paul.bourdelais(AT)gd-ais.com), Nov 04 2008]
(Other) PFGW v3.3.1 [From Paul Bourdelais (pbourdelais(AT)radiantblue.com), Jul 09 2010]
(Other) PFGW v3.3.1 [From Paul Bourdelais (pbourdelais(AT)radiantblue.com), Jul 16 2010]
(Other) PFGW v3.3.1 [From Paul Bourdelais (pbourdelais(AT)radiantblue.com), Aug 23 2010]
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CROSSREFS
| Sequence in context: A059489 A197161 A059852 * A142009 A067393 A113265
Adjacent sequences: A057168 A057169 A057170 * A057172 A057173 A057174
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Sep 15 2000
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EXTENSIONS
| More terms from Kamil Duszenko (kdusz(AT)wp.pl), Jun 23 2003
30133 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 05 2008
a(10) discovered 10/29/08 is a probable prime based on trial factoring to 3.5e13 and Fermat testing base 2. Paul Bourdelais (paul.bourdelais(AT)gd-ais.com), Nov 04 2008
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 (paul.bourdelais(AT)gd-ais.com), Dec 24 2008
a(12)=266863 is a probable prime discovered by Paul Bourdelais (pbourdelais(AT)radiantblue.com), Jul 09 2010
a(13)=277183 is a probable prime discovered by Paul Bourdelais (pbourdelais(AT)radiantblue.com), Jul 16 2010
a(14)=335429 is a probable prime discovered by Paul Bourdelais (pbourdelais(AT)radiantblue.com), Aug 23 2010
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