A286395 - OEIS

%I #21 May 25 2024 14:28:24

%S 1,3,7,8,9,11,15,19,29,55,76,159,266,311,394,908,1732,1875,4335,6334,

%T 7641,16421,33721,139239,157705,160143

%N Numbers k such that (17*10^k + 67)/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 89 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 56w89</a>.

%e 3 is in this sequence because (17*10^3 + 67)/3 = 5689 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 79;

%e a(2) = 3, 5689;

%e a(3) = 7, 56666689;

%e a(4) = 8, 566666689;

%e a(5) = 9, 5666666689; etc.

%t Select[Range[0, 100000], PrimeQ[(17*10^# + 67)/3] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, May 09 2017

%E a(24)-a(26) from _Robert Price_, Jan 24 2019