A293687 - OEIS

%I #37 May 27 2024 02:21:31

%S 2,5,21,23,47,75,107,110,188,261,617,872,965,2735,10145,12572,13364,

%T 14570,195350

%N Numbers k such that (11*10^k - 137)/9 is prime.

%C For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 2 followed by the digits 07 is prime (see Example section).

%C a(20) > 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 12w07</a>.

%e 2 is in this sequence because (11*10^2 - 137)/9 = 107 is prime.

%e Initial terms and associated primes:

%e a(1) = 2, 107;

%e a(2) = 5, 122207;

%e a(3) = 21, 1222222222222222222207;

%e a(4) = 23, 122222222222222222222207;

%e a(5) = 47, 122222222222222222222222222222222222222222222207; etc.

%t Select[Range[2, 100000], PrimeQ[(11*10^# - 137)/9] &]

%o (PARI) isok(k) = isprime((11*10^k - 137)/9); \\ _Michel Marcus_, Nov 15 2017

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Nov 15 2017

%E a(19) from _Robert Price_, Jan 26 2018