A282667 - OEIS

%I #12 Jun 08 2024 05:44:58

%S 1,2,4,8,12,15,21,31,48,151,723,879,1811,3444,5104,5512,5695,6723,

%T 9082,14944,15184,18512,35141,81985,123563,155203,165134,165239

%N Numbers k such that (7*10^k + 107)/3 is prime.

%C For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 3 followed by the digits 69 is prime (see Example section).

%C a(29) > 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 23w69</a>.

%e 4 is in this sequence because (7*10^4 + 107)/3 = 23369 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 59;

%e a(2) = 2, 269;

%e a(3) = 4, 23369;

%e a(4) = 8, 233333369;

%e a(5) = 12, 2333333333369; etc.

%t Select[Range[0, 100000], PrimeQ[(7*10^# + 107)/3] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Feb 20 2017

%E a(25)-a(28) from _Robert Price_, Feb 21 2018