%I #14 May 19 2024 21:55:21
%S 0,1,2,3,4,5,16,19,22,37,58,547,570,817,1068,1909,12809,14470,18209,
%T 33176,33412,42176,49798,89401
%N Numbers k such that 28*10^k + 1 is prime.
%C For k > 0, numbers k such that the digits 28 followed by k-1 occurrences of the digit 0 followed by the digit 1 is prime (see Example section).
%C a(25) > 10^5.
%H Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 280w1</a>.
%e 2 is in this sequence because 28*10^2 + 1 = 2801 is prime.
%e Initial terms and associated primes:
%e a(1) = 0, 29;
%e a(2) = 1, 281;
%e a(3) = 2, 2801;
%e a(4) = 3, 280001;
%e a(5) = 4, 2800001; etc.
%t Select[Range[0, 100000], PrimeQ[28*10^# + 1] &]
%o (PARI) lista(nn) = for(n = 0, nn, if(isprime(28*10^n+1), print1(n, ", "))) \\ _Iain Fox_, Oct 18 2017
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,3
%A _Robert Price_, Oct 16 2017