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A271882 Numbers k such that (10^k + 101)/3 is prime.

%I A271882 #17 May 02 2024 22:54:29
%S A271882 1,2,3,6,9,12,23,39,59,168,198,203,231,449,863,920,1064,1484,1674,
%T A271882 2018,2943,3123,4073,4122,8360,11774,16031,26507,31146,33170,44952,
%U A271882 62402,88020,89687
%N A271882 Numbers k such that (10^k + 101)/3 is prime.
%C A271882 For k > 1, numbers k such that k-2 occurrences of the digit 3 followed by the digits 67 is prime (see Example section).
%C A271882 a(35) > 2*10^5.
%H A271882 Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H A271882 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 3w67</a>.
%e A271882 3 is in this sequence because (10^3+101)/3 = 367 is prime.
%e A271882 Initial terms and associated primes:
%e A271882 a(1) = 1, 37;
%e A271882 a(2) = 2, 67;
%e A271882 a(3) = 3, 367;
%e A271882 a(4) = 6, 333367;
%e A271882 a(5) = 9, 333333367, etc.
%t A271882 Select[Range[0, 100000], PrimeQ[(10^#+101)/3] &]
%o A271882 (PARI) lista(nn) = for(n=1, nn, if(ispseudoprime((10^n+101)/3), print1(n, ", "))); \\ _Altug Alkan_, Apr 16 2016
%Y A271882 Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K A271882 nonn,more
%O A271882 1,2
%A A271882 _Robert Price_, Apr 16 2016