|
%I #12 Sep 08 2022 08:46:13
%S 2,6,12,110,3608,37784
%N Numbers k such that 2*R_k + 9*10^k + 7 is prime, where R_k = 11...11 is the repunit (A002275) of length k.
%C Also, numbers k such that (83*10^k + 61)/9 is prime.
%C Terms from Kamada data.
%C a(7) > 10^5.
%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/9/92229.htm#prime">Prime numbers of the form 922...229</a>.
%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.
%e For k=2, 2*R_2 + 9*10^k + 7 = 22 + 900 + 7 = 929 which is prime.
%t Select[Range[0, 100000], PrimeQ[(83*10^#+61)/9] &]
%o (Magma) [n: n in [0..300] | IsPrime((83*10^n+61) div 9)]; // _Vincenzo Librandi_, Jun 19 2015
%Y Cf. A002275.
%K nonn,more,hard
%O 1,1
%A _Robert Price_, Jun 18 2015
| 