%I #15 Jun 09 2024 22:01:33
%S 0,1,6,7,27,51,67,69,115,153,346,351,1152,1807,2508,4470,4875,5277,
%T 7527,10339,11407,21807,26199,46473,68368,181029
%N Numbers k such that 44*10^k + 3 is prime.
%C For k > 0, numbers k such that the digits 44 followed by k-1 occurrences of the digit 0 followed by the digit 3 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 440w3</a>.
%e 1 is in this sequence because 44*10^1 + 3 = 443 is prime.
%e Initial terms and associated primes:
%e a(1) = 0, 47;
%e a(2) = 1, 443;
%e a(3) = 6, 44000003;
%e a(4) = 7, 440000003;
%e a(5) = 27, 44000000000000000000000000003; etc.
%t Select[Range[0, 100000], PrimeQ[44*10^# + 3] &]
%o (PARI) isok(k) = ispseudoprime(44*10^k + 3) \\ _Altug Alkan_, Aug 27 2017
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,3
%A _Robert Price_, Aug 27 2017
%E a(28) from _Robert Price_, Apr 09 2020