cp's OEIS Frontend

A098088 Numbers k such that 6*R_k - 5 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

%I A098088 #36 Sep 05 2025 00:59:20
%S A098088 2,3,4,10,18,21,22,28,43,66,121,133,178,241,454,553,1600,2175,2978,
%T A098088 3649,7708,8316,10392,12458,21057,26223,48297,64041,84904,92976,95072,
%U A098088 103161,140461,141751,150612,265321,672745
%N A098088 Numbers k such that 6*R_k - 5 is prime, where R_k = 11...1 is the repunit (A002275) of length k.
%C A098088 Also numbers k such that (2*10^k - 17)/3 is prime.
%C A098088 The terms 1600, 2175, 2978 and 3649 correspond to primes. - Joao da Silva (zxawyh66(AT)yahoo.com), Oct 03 2005
%C A098088 a(37) > 3*10^5, _Robert Price_, Oct 19 2023
%H A098088 Makoto Kamada, <a href="https://stdkmd.net/nrr/6/66661.htm#prime">Prime numbers of the form 66...661</a>.
%H A098088 <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>
%F A098088 a(n) = A056658(n) + 1. - Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008
%e A098088 If n = 4 we get ((2*10^4)-17)/3 = 19983/3 = 6661, which is prime.
%t A098088 Do[ If[ PrimeQ[ 2(10^n - 1)/3 - 5], Print[n]], {n, 0, 7000}]
%K A098088 more,nonn,changed
%O A098088 1,1
%A A098088 Julien Peter Benney (jpbenney(AT)ftml.net), Sep 14 2004
%E A098088 a(21)-a(22) from Kamada link by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008
%E A098088 a(23)-a(26) from Kamada link by _Ray Chandler_, Dec 23 2010
%E A098088 a(27) from Kamada link by _Robert Price_, Aug 17 2014
%E A098088 a(28)-a(31) from _Robert Price_, Aug 17 2014
%E A098088 a(32)-a(36) from _Robert Price_, Oct 19 2023
%E A098088 a(37) from Kamada link by _Tyler Busby_, Sep 04 2025