%I #11 Jun 08 2024 05:44:12

%S 4,6,12,14,18,26,40,46,114,138,194,484,889,939,1264,1808,1964,2077,

%T 5929,6512,8892,10862,38120,53664,88822

%N Numbers k such that 39*10^k + 1 is prime.

%C For k > 0, numbers k such that the digits 39 followed by k-1 occurrences of the digit 0 followed by the digit 1 is prime (see Example section).

%C a(26) > 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 390w1</a>.

%e 6 is in this sequence because 39*10^6 + 1 = 39000001 is prime.

%e Initial terms and associated primes:

%e a(1) = 4, 390001;

%e a(2) = 6, 39000001;

%e a(3) = 12, 39000000000001;

%e a(4) = 14, 3900000000000001;

%e a(5) = 18, 39000000000000000001; etc.

%t Select[Range[0, 100000], PrimeQ[39*10^# + 1] &]

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Feb 10 2017