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Numbers k such that 2*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 #35 Jul 13 2023 12:27:48

%S 1,2,3,5,6,7,11,21,30,68,73,169,176,345,823,1021,1191,2073,2755,10717,

%T 14673,16754,17606,81029,120851,167965,200408

%N Numbers k such that 2*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 (8*10^k - 11)/3 is prime.

%C a(28) > 3*10^5. - _Robert Price_, Jul 13 2023

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/2/26663.htm#prime">Prime numbers of the form 266...663</a>.

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

%F a(n) = A101964(n) + 1.

%e For k = 1, 2, 3, 5, 6, 7, we get 23, 263, 2663, 266663, 2666663 and 26666663 which are primes.

%t Do[ If[ PrimeQ[(8*10^n - 11)/3], Print[n]], {n, 0, 10000}]

%Y Cf. A002275, A101964.

%K more,nonn

%O 1,2

%A Julien Peter Benney (jpbenney(AT)ftml.net), Oct 21 2004

%E a(15), a(16) & a(17) from _Ray Chandler_, Nov 04 2004

%E a(18) & a(19) from _Robert G. Wilson v_, Dec 17 2004

%E a(20)-a(23) from Kamada link by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

%E a(24) from Kamada data by _Robert Price_, Jan 17 2015

%E a(25)-a(27) from _Robert Price_, Jul 13 2023