%I #14 Jun 08 2024 15:41:23

%S 0,2,4,9,14,20,28,33,156,285,302,1121,1300,2540,3873,4706,5297,7292,

%T 11086,15928,16203,17267,17793,19326,32009,67659

%N Numbers k such that (292*10^k - 1)/3 is prime.

%C Numbers k such that the digits 97 followed by k occurrences of the digit 3 is prime (see Example section).

%C a(27) > 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 973w3</a>.

%e 2 is in this sequence because (292*10^2 - 1)/3 = 9733 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 97;

%e a(2) = 2, 9733;

%e a(3) = 4, 973333;

%e a(4) = 9, 97333333333;

%e a(5) = 14, 9733333333333333; etc.

%t Select[Range[0, 100000], PrimeQ[(292*10^# - 1)/3] &]

%o (PARI) isok(n) = isprime((292*10^n - 1)/3); \\ _Michel Marcus_, Jan 21 2017

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Jan 21 2017