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A273944 Numbers k such that (266*10^k - 17)/3 is prime.

%I A273944 #40 May 02 2024 04:28:02
%S A273944 0,1,2,3,7,8,11,14,24,29,50,78,99,192,226,519,613,651,1492,3720,6567,
%T A273944 6791,7226,8471,9050,13521,14255,33529,44072,47844,64102,112930,
%U A273944 116024,122872,138328,140681,268407
%N A273944 Numbers k such that (266*10^k - 17)/3 is prime.
%C A273944 For k > 1, numbers k such that the digits 88 followed by k-1 occurrences of the digit 6 followed by the digit 1 is prime (see Example section).
%C A273944 a(38) > 3*10^5.
%H A273944 Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H A273944 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 886w1</a>.
%e A273944 3 is in this sequence because (266*10^3-17)/3 = 88661 is prime.
%e A273944 Initial terms and associated primes:
%e A273944 a(1) = 0, 83;
%e A273944 a(2) = 1, 881;
%e A273944 a(3) = 2, 8861;
%e A273944 a(4) = 3, 88661;
%e A273944 a(5) = 7, 886666661, etc.
%t A273944 Select[Range[0, 100000], PrimeQ[(266*10^# - 17)/3] &]
%o A273944 (PARI) isok(n) = isprime((266*10^n - 17)/3); \\ _Michel Marcus_, Jun 18 2016
%Y A273944 Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K A273944 nonn,more
%O A273944 1,3
%A A273944 _Robert Price_, Jun 17 2016
%E A273944 a(32)-a(36) from _Robert Price_, Jul 16 2020
%E A273944 a(37) from _Robert Price_, Jun 21 2023