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%I #13 May 02 2024 04:24:32
%S 0,2,3,4,18,21,36,58,68,78,84,94,150,178,190,591,686,812,840,2308,
%T 2530,2884,4311,6134,7695,8004,8109,9777,15570,17505
%N Numbers k such that 16*10^k + 1 is prime.
%C For k > 1, numbers k such that the digits 16 followed by k-1 occurrences of the digit 0 followed by the digit 1 is prime (see Example section).
%C a(31) > 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 160w1</a>.
%e 4 is in this sequence because 16*10^4+1 = 160001 is prime.
%e Initial terms and associated primes:
%e a(1) = 0, 17;
%e a(2) = 2, 1601;
%e a(3) = 3, 16001;
%e a(4) = 4, 160001;
%e a(5) = 18, 16000000000000000001. etc.
%t Select[Range[0, 100000], PrimeQ[16*10^#+1] &]
%o (PARI) is(n)=ispseudoprime(16*10^n+1) \\ _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_, May 12 2016