%I #19 Jun 01 2024 12:42:10
%S 1,2,4,5,7,16,31,34,44,68,145,158,227,499,643,970,1004,1951,2923,3092,
%T 28069,48334,76262
%N Numbers k such that (73*10^k + 413)/9 is prime.
%C For k > 1, numbers k such that the digit 8 followed by k-2 occurrences of the digit 1 followed by the digits 57 is prime (see Example section).
%C a(24) > 2*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 81w57</a>.
%e 4 is in this sequence because (73*10^4 + 413)/9 = 81157 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 127;
%e a(2) = 2, 857;
%e a(3) = 4, 81157;
%e a(4) = 5, 811157;
%e a(5) = 7, 81111157; etc.
%t Select[Range[0, 100000], PrimeQ[(73*10^# + 413)/9] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,2
%A _Robert Price_, Oct 06 2017
|