A256933 - OEIS

%I #17 Sep 08 2022 08:46:12

%S 1,2,11,62,157,170,251,500,2275,7525,12230,13658,54727,183227,212779

%N Numbers k such that R_(k+2) + 7*10^k is prime, where R_k = 11...1 is the repunit (A002275) of length k.

%C Also, numbers k such that (163*10^k - 1)/9  is prime.

%C Terms from Kamada.

%C a(16) > 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/1/18111.htm#prime">Prime numbers of the form 1811...11</a>.

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

%e For k=2, R_4 + 7*10^2 = 1111 + 700 = 1811 which is prime.

%t Select[Range[0, 250000], PrimeQ[(163*10^#-1)/9 ] &]

%o (Magma) [n: n in [0..300] | IsPrime((163*10^n-1) div 9)]; // _Vincenzo Librandi_, Apr 14 2015

%o (PARI) for(n=0,300,if(isprime((163*10^n-1)/9),print1(n,", "))) \\ _Derek Orr_, Apr 14 2015

%Y Cf. A002275.

%K more,hard,nonn

%O 1,2

%A _Robert Price_, Apr 13 2015