%I #16 Jun 01 2023 02:46:03
%S 0,1,2,3,4,8,44,53,79,89,95,120,224,259,290,488,725,821,1815,3096,
%T 3100,3404,5909,8054,11879,17298,25588,41516,127324,191900
%N Numbers k such that (112*10^k + 17)/3 is prime.
%C For k>0, numbers k such that the digits 37 followed by k-1 occurrences of the digit 3 followed by the digit 9 is prime (see Example section).
%C a(31) > 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 373w9</a>.
%e 3 is in this sequence because (112*10^3+17)/3 = 37339 is prime.
%e Initial terms and primes associated:
%e a(1) = 0, 43;
%e a(2) = 1, 379:
%e a(3) = 2, 3739;
%e a(4) = 3, 37339;
%e a(5) = 4, 373339, etc.
%t Select[Range[0, 100000], PrimeQ[(112*10^# + 17)/3] &]
%o (PARI) is(n)=ispseudoprime((112*10^n + 17)/3) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more
%O 1,3
%A _Robert Price_, May 14 2016
%E a(29)-a(30) from _Robert Price_, Mar 05 2020
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