A295327 - OEIS

%I #15 May 05 2024 00:21:07

%S 1,13,16,19,23,25,29,30,34,53,61,89,111,191,376,1918,2889,12304,17939,

%T 18053,31740,56575,65899

%N Numbers k such that 3*10^k - 13 is prime.

%C For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 9 followed by the digits 87 is prime (see Example section).

%C a(24) > 2*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 29w87</a>.

%e 1 is in this sequence because 3*10^1 - 13 = 17 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 17;

%e a(2) = 13, 29999999999987;

%e a(3) = 16, 29999999999999987;

%e a(4) = 19, 29999999999999999987;

%e a(5) = 23, 299999999999999999999987; etc.

%t Select[Range[1, 100000], PrimeQ[3*10^# - 13] &]

%o (PARI) isok(k) = isprime(3*10^k - 13); \\ _Michel Marcus_, Nov 20 2017

%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Nov 19 2017