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A274331 Numbers k such that (148*10^k - 1)/3 is prime.

%I A274331 #14 May 26 2024 14:58:53
%S A274331 2,3,4,5,9,27,35,44,88,104,205,290,302,381,400,686,917,1150,2278,2757,
%T A274331 3220,3316,7469,9535,21442,46409,103718,123688,147139
%N A274331 Numbers k such that (148*10^k - 1)/3 is prime.
%C A274331 Numbers k such that the digits 49 followed by k occurrences of the digit 3 is prime (see Example section).
%C A274331 a(30) > 2*10^5.
%H A274331 Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H A274331 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 493w</a>.
%e A274331 3 is in this sequence because (148*10^3-1)/3 = 233329 is prime.
%e A274331 Initial terms and associated primes:
%e A274331 a(1) = 2, 4933;
%e A274331 a(2) = 3, 49333;
%e A274331 a(3) = 4, 493333;
%e A274331 a(4) = 5, 4933333;
%e A274331 a(5) = 9, 49333333333, etc.
%t A274331 Select[Range[0, 100000], PrimeQ[(148*10^# - 1)/3] &]
%o A274331 (PARI) is(n)=ispseudoprime((148*10^n - 1)/3) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y A274331 Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K A274331 nonn,more
%O A274331 1,1
%A A274331 _Robert Price_, Jun 18 2016
%E A274331 a(27)-a(29) from _Robert Price_, Mar 18 2020