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Numbers k such that 5*R_k + 10^k - 4 is prime, where R_k = 11...11 is the repunit (A002275) of length k.
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%I #23 Sep 14 2024 02:23:00

%S 1,2,4,20,32,400,562,7016,37684

%N Numbers k such that 5*R_k + 10^k - 4 is prime, where R_k = 11...11 is the repunit (A002275) of length k.

%C Also, numbers k such that (14*10^k - 41)/9 is prime.

%C Terms from Kamada data.

%C a(10) > 10^5.

%C Per Kamada link, 211262, 222718, 250336 are also terms, found by _Serge Batalov_ - _Michael S. Branicky_, Sep 13 2024

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/abbba.htm">Near-repdigit numbers of the form ABB...BBA</a>.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/1/15551.htm#prime">Prime numbers of the form 155...551</a>.

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

%e For k=4, 5*R_4 + 10^k - 4 = 5555 + 10000 - 4 = 15551 which is prime.

%t Select[Range[100000], PrimeQ[(14*10^#-41)/9] &]

%Y Cf. A002275.

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Jun 18 2015