A288484 - OEIS

%I #20 May 25 2024 17:41:20

%S 0,1,2,9,16,23,33,40,42,45,48,137,176,553,775,2072,3259,7773,9457,

%T 17638,20838,22277,32672,47983,52308,54765,117229,228177

%N Numbers k such that (298*10^k - 7)/3 is prime.

%C For k > 0, numbers k such that the digits 99 followed by k-1 occurrences of the digit 3 followed by the digit 1 is prime (see Example section).

%C a(29) > 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 993w1</a>.

%e 2 is in this sequence because (298*10^2 - 7)/3 = 9931 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 97;

%e a(2) = 1, 991;

%e a(3) = 2, 9931;

%e a(4) = 9, 99333333331;

%e a(5) = 16, 993333333333333331; etc.

%t Select[Range[0, 100000], PrimeQ[(298*10^# - 7)/3] &]

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

%K nonn,more,hard

%O 1,3

%A _Robert Price_, Jun 09 2017

%E a(27) from _Robert Price_, Jun 09 2020

%E a(28) from _Robert Price_, Jun 21 2023