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%I #17 May 25 2024 19:09:42
%S 1,2,15,17,26,41,56,59,121,137,224,506,611,836,937,1079,1829,2315,
%T 2666,2879,6661,7167,14021,15459,32924,73346,176815,177302
%N Numbers k such that (101*10^k - 17)/3 is prime.
%C Numbers k such that the digits 33 followed by k-1 occurrences of the digit 6 followed by the digit 1 is prime (see Example section).
%C a(29) > 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 336w1</a>.
%e 2 is in this sequence because (101*10^2 - 17)/3 = 3361 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 331;
%e a(2) = 2, 3361;
%e a(3) = 15, 33666666666666661;
%e a(4) = 17, 3366666666666666661;
%e a(5) = 26, 3366666666666666666666666661, etc.
%t Select[Range[0, 100000], PrimeQ[(101*10^# - 17)/3] &]
%o (PARI) is(n)=ispseudoprime((101*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 1,2
%A _Robert Price_, Aug 18 2016
%E a(27)-a(28) from _Robert Price_, Feb 05 2020