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%I #13 Jan 17 2019 13:44:09
%S 2,4,8,10,14,16,29,106,179,197,365,371,557,857,862,1163,1454,2206,
%T 5075,22384,149999,196792
%N Numbers k such that (38*10^k + 691)/9 is prime.
%C For k > 1, numbers such that the digit 4 followed by k - 2 occurrences of the digit 2 followed by the digits 99 is prime (see Example section).
%C There are no multiples of 3 in the sequence, since (38 * 10^k + 691)/9 is a multiple of 3 if k is.
%C a(23) > 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/primedifficulty.txt">Search for 42w99.</a>
%e 4 is in this sequence because (38*10^4 + 691)/9 = 42299 is prime.
%e Initial terms and primes associated:
%e a(1) = 2, 499;
%e a(2) = 4, 42299;
%e a(3) = 8, 422222299;
%e a(4) = 10; 42222222299;
%e a(5) = 14, 422222222222299; etc.
%t Select[Range[1000], PrimeQ[(38*10^# + 691)/9] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,1
%A _Robert Price_, Aug 03 2017
%E a(21)-a(22) from _Robert Price_, Oct 31 2018
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