A295329 - OEIS

%I #17 May 05 2024 00:21:15

%S 0,1,4,6,9,10,24,94,136,144,186,337,390,448,564,916,1384,2052,5424,

%T 28636,39574,65532

%N Numbers k such that (28*10^k + 359)/9 is prime.

%C For k > 1, numbers k such that the digit 3 followed by k-2 occurrences of the digit 1 followed by the digits 51 is prime (see Example section).

%C a(23) > 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 31w51</a>.

%e 1 is in this sequence because (28*10^1 + 359)/9 = 71 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 43;

%e a(2) = 1, 71;

%e a(3) = 4, 31151;

%e a(4) = 6, 3111151;

%e a(5) = 9, 3111111151; etc.

%t Select[Range[0, 100000], PrimeQ[(28*10^# + 359)/9] &]

%o (PARI) isok(k) = isprime((28*10^k + 359)/9); \\ _Michel Marcus_, Nov 20 2017

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

%K nonn,more,hard

%O 1,3

%A _Robert Price_, Nov 19 2017