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Numbers k such that 13*10^k + 1 is prime.
1

%I #8 May 19 2024 21:54:47

%S 1,2,3,7,16,53,95,105,125,163,358,423,562,1774,3459,13957,17962,51179,

%T 65963,72808

%N Numbers k such that 13*10^k + 1 is prime.

%C For k > 0, numbers k such that the digits 13 followed by k-1 occurrences of the digit 0 followed by the digit 1 is prime (see Example section).

%C a(21) > 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 130w1</a>.

%e 2 is in this sequence because 13*10^3 + 1 = 1301 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 131;

%e a(2) = 2, 1301;

%e a(3) = 3, 13001;

%e a(4) = 7, 130000001;

%e a(5) = 16, 130000000000000001; etc.

%t Select[Range[0, 100000], PrimeQ[13*10^# + 1] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Jun 22 2017