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Numbers k such that 4*10^k + 6*R_k - 3 is prime, where R_k = 11...1 is the repunit (A002275) of length k.
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%I #36 May 31 2023 15:54:55

%S 1,2,3,4,6,7,8,12,23,59,75,144,204,268,760,1216,1430,1506,1509,2804,

%T 2924,3201,3305,5753,9268,11279,19677,23414,28627,31362,42299,49119,

%U 63747,81767,111443,263720,264791

%N Numbers k such that 4*10^k + 6*R_k - 3 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

%C Also numbers k such that (14*10^k - 11)/3 is a prime number.

%C a(38) > 3*10^5. - _Robert Price_, Mar 30 2015

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/4/46663.htm#prime">Prime numbers of the form 466...663</a>.

%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.

%F a(n) = A101730(n) + 1.

%e For n = 1, 2, 3, 4, 6, 7, 8 are members since 43, 463, 4663, 46663, 4666663, 46666663 and 466666663 are primes.

%t Do[ If[ PrimeQ[(14*10^n - 11)/3], Print[n]], {n, 0, 10000}] (* _Robert G. Wilson v_, Dec 17 2004 *)

%Y Cf. A101730.

%K more,nonn

%O 1,2

%A Julien Peter Benney (jpbenney(AT)ftml.net), Nov 07 2004

%E a(15) - a(21) from _Robert G. Wilson v_, Dec 22 2004

%E a(22) - a(25) from _Robert G. Wilson v_, Jan 17 2005

%E a(26)-a(27) from Kamada link by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

%E a(28)-a(29) from Kamada data by _Robert Price_, Dec 08 2010

%E a(30)-a(32) from Erik Branger, May 01 2013, submitted by _Ray Chandler_, Aug 16 2013

%E a(33)-a(34) from Kamada data by _Robert Price_, Mar 30 2015

%E a(35)-a(37) from _Robert Price_, May 31 2023