A282635 - OEIS

%I #23 May 25 2024 14:17:00

%S 3,9,10,28,41,58,62,86,192,209,566,1227,1566,1995,2003,3654,4271,6107,

%T 6281,8997,24412,32970,65944,85782,112742,115910,141718

%N Numbers k such that (11*10^k - 131)/3 is prime.

%C For k > 1, numbers k such that the digit 3 followed by k-2 occurrences of the digit 6 followed by the digits 23 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 36w23</a>.

%e 3 is in this sequence because (11*10^3 - 131)/3 = 3623 is prime.

%e Initial terms and associated primes:

%e a(1) = 3, 3623;

%e a(2) = 9, 3666666623;

%e a(3) = 10, 36666666623;

%e a(4) = 28, 36666666666666666666666666623;

%e a(5) = 41, 366666666666666666666666666666666666666623; etc.

%t Select[Range[2, 100000], PrimeQ[(11*10^# - 131)/3] &]

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Feb 23 2017

%E a(25)-a(27) from _Robert Price_, Sep 28 2018