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%I #33 Apr 14 2024 03:44:54
%S 1,2,6,8,9,11,20,23,41,63,66,119,122,149,252,284,305,592,746,875,1204,
%T 1364,2240,2403,5106,5776,5813,12456,14235,39606,55544,84239,275922
%N Numbers k such that 6*R_k + 1 is a prime, where R_k = 11...1 is the repunit (A002275) of length k.
%C Also numbers k such that (2*10^k + 1)/3 is prime.
%C These numbers form a near-repdigit sequence (6)w7.
%C All the terms from k = 2403 through 14235 correspond to primes. - Joao da Silva (zxawyh66(AT)yahoo.com), Oct 03 2005
%H Makoto Kamada, <a href="https://stdkmd.net/nrr/6/66667.htm#prime">Prime numbers of the form 66...667</a>.
%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>
%F a(n) = A056657(n) + 1.
%e k = 9 gives 2000000001/3 = 666666667, which is prime.
%e k = 20 gives 66666666666666666667, which is prime.
%t Select[Range@ 2500, PrimeQ[FromDigits@ Table[6, {#}] + 1] &] (* or *)
%t Select[Range@ 2500, PrimeQ[2 (10^# - 1)/3 + 1] &] (* _Michael De Vlieger_, Jul 04 2016 *)
%Y Cf. A002275, A056657, A093170, A096503, A096504, A096505, A096506, A096508.
%K nonn,changed
%O 1,2
%A _Labos Elemer_, Jul 12 2004
%E More terms from Julien Peter Benney (jpbenney(AT)ftml.net), Sep 14 2004
%E 39606 and 55544 from _Serge Batalov_, Jun 2009
%E 84239 from _Serge Batalov_, Jul 06 2009 confirmed as next term by _Ray Chandler_, Feb 23 2012
%E a(33) from Kamada data by _Tyler Busby_, Apr 14 2024
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