|
%I #14 Jun 21 2023 14:27:58
%S 0,1,2,4,5,8,11,21,25,105,191,305,463,704,1320,1404,1580,1675,2215,
%T 3475,6323,10560,28817,30356,98198
%N Numbers k such that 12*10^k - 7 is prime.
%C For k > 1, numbers such that the digits 11 followed by k-1 occurrences of the digit 9 followed by the digit 3 is prime (see Example section).
%C a(26) > 3*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/primedifficulty.txt">Search for 119w3</a>.
%e 2 is in this sequence because 12*10^2 - 7 = 1193 is prime.
%e Initial terms and primes associated:
%e a(1) = 0, 5;
%e a(2) = 1, 113;
%e a(3) = 2, 1193;
%e a(4) = 4, 119993;
%e a(5) = 5, 1199993; etc.
%t Select[Range[0, 100000], PrimeQ[12*10^# - 7 ] &]
%o (PARI) isok(k) = isprime(12*10^k - 7); \\ _Michel Marcus_, Nov 13 2017
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,3
%A _Robert Price_, Nov 12 2017
|
