login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Numbers k such that (19*10^k + 413)/9 is prime.
0

%I #11 May 25 2024 16:58:00

%S 1,2,4,7,11,22,28,29,38,62,316,989,1532,2068,2495,3431,4775,9082,

%T 14935,15572,39511,43283,66748

%N Numbers k such that (19*10^k + 413)/9 is prime.

%C For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 2 followed by the digits 57 is prime (see Example section).

%C a(24) > 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 21w57</a>.

%e 2 is in this sequence because (19*10^2 + 413)/9 = 257 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 67;

%e a(2) = 2, 257;

%e a(3) = 4, 21157;

%e a(4) = 7, 21111157;

%e a(5) = 11, 211111111157; etc.

%t Select[Range[0, 100000], PrimeQ[(19*10^# + 413)/9] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Oct 14 2017