|
%I #24 Sep 08 2022 08:46:12
%S 0,1,2,5,7,14,32,65,163,398,485,1799,1852,3326,3692,7226,12743,15313,
%T 110405,120395,132337,140357,153025,194150
%N Numbers k such that 3*R_(k+2) + 4*10^k is prime, where R_k = 11...1 is the repunit (A002275) of length k.
%C Also, numbers k such that (112*10^k - 1)/3 is prime.
%C Terms from Kamada.
%C a(25) > 250000.
%H Makoto Kamada, <a href="https://stdkmd.net/nrr/abaaa.htm">Near-repdigit numbers of the form ABAA...AA</a>.
%H Makoto Kamada, <a href="https://stdkmd.net/nrr/3/37333.htm#prime">Prime numbers of the form 3733...33</a>.
%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.
%e For k=2, 3*R_4 + 4*10^2 = 3333 + 400 = 3733 which is prime.
%t Select[Range[0, 250000], PrimeQ[(112*10^#-1)/3 ] &]
%o (PARI) for(n=0,500,if(isprime((112*10^n-1)/3),print1(n,", "))) \\ _Derek Orr_, Apr 14 2015
%o (Magma) [n: n in [0..300] | IsPrime((112*10^n-1) div 3)]; // _Vincenzo Librandi_, Apr 15 2015
%Y Cf. A002275.
%K more,hard,nonn
%O 1,3
%A _Robert Price_, Apr 14 2015
|
