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A270890 Numbers k such that (8*10^k + 49)/3 is prime.

%I A270890 #18 May 26 2024 14:58:27
%S A270890 0,1,2,3,4,5,6,10,24,33,34,35,45,52,56,62,65,103,166,424,886,1418,
%T A270890 1825,4895,5715,7011,7810,9097,12773,14746,20085,25359,27967,46629,
%U A270890 48507,68722,74944,102541,118960,157368
%N A270890 Numbers k such that (8*10^k + 49)/3 is prime.
%C A270890 For k > 2, numbers k such that the digit 2 followed by k-3 occurrences of the digit 6 followed by the digits 83 is prime (see Example section).
%C A270890 a(41) > 3*10^5.
%H A270890 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 26w83</a>.
%e A270890 3 is in this sequence because (8*10^3 + 49)/3 = 2683 is prime.
%e A270890 Initial terms and associated primes:
%e A270890 a(1) = 0, 19;
%e A270890 a(2) = 1, 43;
%e A270890 a(3) = 2, 283;
%e A270890 a(4) = 3, 2683;
%e A270890 a(5) = 4, 26683;
%e A270890 a(6) = 5, 266683, etc.
%t A270890 Select[Range[0, 100000], PrimeQ[(8*10^# + 49)/3] &]
%o A270890 (PARI) is(n)=isprime((8*10^n + 49)/3) \\ _Charles R Greathouse IV_, Feb 16 2017
%Y A270890 Cf. A056654, A268448, A269303, A270339, A270613, A270831.
%K A270890 nonn,more
%O A270890 1,3
%A A270890 _Robert Price_, Mar 25 2016
%E A270890 a(38)-a(40) from _Robert Price_, May 23 2020