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A001562
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Numbers n such that (10^n + 1)/11 is a prime.
(Formerly M3767 N1537)
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5
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5, 7, 19, 31, 53, 67, 293, 641, 2137, 3011, 268207
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The a(10) to a(11) gap represents the largest relative gap seen so far in searching Repunits with bases between -12 and 12. On average, there should have been 4 more primes added to this sequence by a(11), instead of just 1. [From Paul Bourdelais (pbourdelais(AT)radiantblue.com), Feb 11 2010]
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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, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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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.
S. S. Wagstaff, Jr., The Cunningham Project
Eric Weisstein's World of Mathematics, Repunit
H. Lifchitz, Mersenne and Fermat primes field
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MATHEMATICA
| lst={}; Do[If[PrimeQ[(10^n+1)/11], AppendTo[lst, n]], {n, 0, 10^4}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 10 2008]
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PROG
| (Other) PFGW v3.3.1 [From Paul Bourdelais (pbourdelais(AT)radiantblue.com), Feb 11 2010]
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CROSSREFS
| Equals 2*A054416 + 1.
Sequence in context: A128335 A023246 A022889 * A163386 A200178 A064101
Adjacent sequences: A001559 A001560 A001561 * A001563 A001564 A001565
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KEYWORD
| nonn,hard
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| a(11)=268207 is a probable prime discovered by Paul Bourdelais (pbourdelais(AT)radiantblue.com), Feb 11 2010
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