A294378 - OEIS

%I #11 May 19 2024 21:55:41

%S 1,2,5,11,24,49,50,59,67,71,91,605,726,899,1214,3307,3409,3961,11426,

%T 30096,70241,80089,108446

%N Numbers k such that (197*10^k - 11)/3 is prime.

%C For k > 0, numbers k such that the digits 65 followed by k-1 occurrences of the digit 6 followed by the digit 3 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 656w3</a>.

%e 2 is in this sequence because (197*10^2 - 11)/3 = 6563 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 653;

%e a(2) = 2, 6563;

%e a(3) = 5, 6566663;

%e a(4) = 11, 6566666666663;

%e a(5) = 24, 65666666666666666666666663; etc.

%t Select[Range[0, 100000], PrimeQ[(197*10^# - 11)/3] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Oct 29 2017

%E a(23) from _Robert Price_, Mar 22 2020