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 A096507 Numbers k such that 6*R_k + 1 is a prime, where R_k = 11...1 is the repunit (A002275) of length k. 13
 1, 2, 6, 8, 9, 11, 20, 23, 41, 63, 66, 119, 122, 149, 252, 284, 305, 592, 746, 875, 1204, 1364, 2240, 2403, 5106, 5776, 5813, 12456, 14235, 39606, 55544, 84239, 275922 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also numbers k such that (2*10^k + 1)/3 is prime. These numbers form a near-repdigit sequence (6)w7. All the terms from k = 2403 through 14235 correspond to primes. - Joao da Silva (zxawyh66(AT)yahoo.com), Oct 03 2005 LINKS Table of n, a(n) for n=1..33. Makoto Kamada, Prime numbers of the form 66...667. Index entries for primes involving repunits FORMULA a(n) = A056657(n) + 1. EXAMPLE k = 9 gives 2000000001/3 = 666666667, which is prime. k = 20 gives 66666666666666666667, which is prime. MATHEMATICA Select[Range@ 2500, PrimeQ[FromDigits@ Table[6, {#}] + 1] &] (* or *) Select[Range@ 2500, PrimeQ[2 (10^# - 1)/3 + 1] &] (* Michael De Vlieger, Jul 04 2016 *) CROSSREFS Cf. A002275, A056657, A093170, A096503, A096504, A096505, A096506, A096508. Sequence in context: A043341 A023714 A355274 * A288428 A050675 A262981 Adjacent sequences: A096504 A096505 A096506 * A096508 A096509 A096510 KEYWORD nonn AUTHOR Labos Elemer, Jul 12 2004 EXTENSIONS More terms from Julien Peter Benney (jpbenney(AT)ftml.net), Sep 14 2004 39606 and 55544 from Serge Batalov, Jun 2009 84239 from Serge Batalov, Jul 06 2009 confirmed as next term by Ray Chandler, Feb 23 2012 a(33) from Kamada data by Tyler Busby, Apr 14 2024 STATUS approved

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Last modified August 9 04:25 EDT 2024. Contains 375027 sequences. (Running on oeis4.)