A278418 - OEIS

%I #17 Jun 08 2024 15:41:01

%S 1,2,4,10,28,31,32,38,68,134,158,254,311,337,392,874,2747,3502,4735,

%T 6142,14140,17095,20066,21104,26743

%N Numbers k such that (83*10^k - 29) / 9 is prime.

%C For k > 1, numbers k such that the digit 9 followed by k-2 occurrences of the digit 2 followed by the digits 19 is prime (see Example section).

%C a(26) > 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 92w19</a>.

%e 4 is in this sequence because (83*10^4 - 29) / 9 = 92219 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 89;

%e a(2) = 2, 919;

%e a(3) = 4, 92219;

%e a(4) = 10, 92222222219;

%e a(5) = 28, 92222222222222222222222222219; etc.

%t Select[Range[0, 100000], PrimeQ[(83*10^# - 29) / 9] &]

%o (PARI) isok(n) = isprime((83*10^n - 29)/9); \\ _Michel Marcus_, Nov 21 2016

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Nov 21 2016