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Numbers k such that 80*R_k + 7 is prime, where R_k = 11...1 is the repunit (A002275) of length k.
2

%I #24 Jul 04 2021 22:10:28

%S 0,2,3,5,8,11,71,117,123,189,243,303,356,1421,2690,5537,7580,21905,

%T 32175,44357

%N Numbers k such that 80*R_k + 7 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

%C Also numbers k such that (8*10^(k+1)-17)/9 is prime.

%C a(21) > 10^5. - _Robert Price_, May 20 2014

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/8/88887.htm#prime">Prime numbers of the form 88...887</a>.

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

%F a(n) = A096846(n) - 1.

%t Do[ If[ PrimeQ[80*(10^n - 1)/9 + 7], Print[n]], {n, 0, 5000}]

%Y Cf. A002275, A093171, A096846.

%K hard,nonn,more

%O 1,2

%A _Robert G. Wilson v_, Aug 10 2000

%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

%E a(18)-a(20) derived from A096846 by _Robert Price_, May 20 2014