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%I #27 May 02 2024 04:26:49
%S 1,2,3,5,16,18,22,31,40,98,99,192,233,367,501,1102,1381,1416,2018,
%T 6156,6860,7377,14004,16634,21422,27654,85473,260256,265052,274251
%N Numbers k such that (16*10^k - 91)/3 is prime.
%C For k > 1, numbers k such that the digit 5 followed by k-1 occurrences of the digit 3 followed by the digits 03 is prime (see Example section).
%C a(31) > 3*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 53w03</a>.
%e 3 is in this sequence because (16*10^3 - 91)/3 = 5303 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 23;
%e a(2) = 2, 503;
%e a(3) = 3, 5303;
%e a(4) = 5, 533303;
%e a(5) = 16, 53333333333333303, etc.
%t Select[Range[0, 100000], PrimeQ[(16*10^# - 91)/3] &]
%o (PARI) is(n)=ispseudoprime((16*10^n - 91)/3) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more
%O 1,2
%A _Robert Price_, Jun 22 2016
%E a(28)-a(30) from _Robert Price_, Jun 01 2023