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A276311 Numbers k such that (13*10^k + 197)/3 is prime.

%I A276311 #16 May 26 2024 16:03:49
%S A276311 1,2,4,5,17,21,23,28,41,43,51,59,105,115,131,273,585,1519,2303,4791,
%T A276311 4921,6019,7833,25711,27319,32497,37975,49381,87199
%N A276311 Numbers k such that (13*10^k + 197)/3 is prime.
%C A276311 For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 3 followed by the digits 99 is prime (see the Example section).
%C A276311 a(30) > 10^5.
%H A276311 Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H A276311 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 43w99</a>.
%e A276311 4 is in this sequence because (13*10^4 + 197)/3 = 43399 is prime.
%e A276311 Initial terms and associated primes:
%e A276311 a(1) = 1, 109;
%e A276311 a(2) = 2, 499;
%e A276311 a(3) = 4, 43399;
%e A276311 a(4) = 5, 433399;
%e A276311 a(5) = 17, 433333333333333399, etc.
%t A276311 Select[Range[0, 100000], PrimeQ[(13*10^# + 197)/3] &]
%o A276311 (PARI) is(n)=ispseudoprime((13*10^n+197)/3) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y A276311 Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K A276311 nonn,more
%O A276311 1,2
%A A276311 _Robert Price_, Aug 29 2016