A286177 - OEIS

%I #12 Jun 10 2024 08:44:00

%S 1,3,8,9,14,17,29,43,48,72,78,132,312,894,968,5030,5108,9008,11989,

%T 12903,26767,28159,30564,39619,44250,54537,77427

%N Numbers k such that (17*10^k - 47)/3 is prime.

%C For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 6 followed by the digits 51 is prime (see Example section).

%C a(28) > 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 56w51</a>.

%e 3 is in this sequence because (17*10^3 - 47)/3 = 5651 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 41;

%e a(2) = 3, 5651;

%e a(3) = 8, 566666651;

%e a(4) = 9, 5666666651;

%e a(5) = 14, 566666666666651; etc.

%t Select[Range[1, 100000], PrimeQ[(17*10^# - 47)/3] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, May 03 2017