A289536 - OEIS

%I #17 Jun 06 2024 23:23:49

%S 2,3,5,10,13,14,22,31,47,57,64,71,86,911,1012,1855,2111,4920,5838,

%T 9238,185221,292619

%N Numbers k such that (4*10^k - 91)/3 is prime.

%C For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 3 followed by the digits 03 is prime (see Example section).

%C a(23) > 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 13w03</a>.

%e 3 is in this sequence because (4*10^3 - 91)/3 = 1303 is prime.

%e Initial terms and associated primes:

%e a(1) = 2, 103;

%e a(2) = 3, 1303;

%e a(3) = 5, 133303;

%e a(4) = 10, 13333333303;

%e a(5) = 13, 13333333333303; etc.

%t Select[Range[2, 100000], PrimeQ[(4*10^# - 91)/3] &]

%o (PARI) isok(k) = ispseudoprime((4*10^k - 91)/3); \\ _Altug Alkan_, Mar 27 2018

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Jul 07 2017

%E a(21) from _Robert Price_, Mar 27 2018

%E a(22) from _Robert Price_, Jul 02 2023