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A270929 Numbers k such that (16*10^k - 31)/3 is prime.

%I A270929 #22 Jun 06 2024 23:24:25
%S A270929 1,2,3,4,15,20,24,32,38,40,63,93,104,194,208,514,535,600,928,1300,
%T A270929 1485,1780,2058,3060,3356,3721,6662,11552,15482,23000,27375,34748,
%U A270929 57219,61251,85221,99656,103214,103244,276537
%N A270929 Numbers k such that (16*10^k - 31)/3 is prime.
%C A270929 For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 3 followed by the digits 23 is prime (see Example section).
%C A270929 a(40) > 3*10^5. - _Robert Price_, Jul 13 2023
%H A270929 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 53w23</a>.
%e A270929 3 is in this sequence because (16*10^3 - 31)/3 = 5323 is prime.
%e A270929 Initial terms and associated primes:
%e A270929 a(1) = 1, 43;
%e A270929 a(2) = 2, 523;
%e A270929 a(3) = 3, 5323;
%e A270929 a(4) = 4, 53323;
%e A270929 a(5) = 15, 5333333333333323;
%e A270929 a(6) = 20, 533333333333333333323, etc.
%t A270929 Select[Range[0, 100000], PrimeQ[(16*10^# - 31)/3] &]
%o A270929 (PARI) isok(n) = ispseudoprime((16*10^n - 31)/3); \\ _Michel Marcus_, Mar 26 2016
%Y A270929 Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890.
%K A270929 nonn,base,more
%O A270929 1,2
%A A270929 _Robert Price_, Mar 26 2016
%E A270929 a(37)-a(38) from _Robert Price_, Mar 03 2019
%E A270929 a(39) from _Robert Price_, Jul 13 2023