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Numbers k such that 3*10^k + 13 is prime.
0

%I #14 May 19 2024 21:54:55

%S 1,2,4,10,12,13,26,37,56,66,288,404,3495,3824,7780,14824,17928,18680,

%T 21414,23782,25392,34749,36180,46316,48477,63522,73962,89206,139722,

%U 172812,184110

%N Numbers k such that 3*10^k + 13 is prime.

%C For k > 1, numbers k such that the digit 3 followed by k-2 occurrences of the digit 0 followed by the digits 13 is prime (see Example section).

%C a(32) > 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 30w13</a>.

%e 4 is in this sequence because 3*10^4 + 13 = 30013 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 43;

%e a(2) = 2, 313;

%e a(3) = 4, 30013;

%e a(4) = 10; 30000000013;

%e a(5) = 12, 3000000000013; etc.

%t Select[Range[0, 100000], PrimeQ[3*10^# + 13] &]

%o (PARI) lista(nn) = for(n=1, nn, if(ispseudoprime(3*10^n + 13), print1(n, ", "))); \\ _Altug Alkan_, Aug 03 2017

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Aug 03 2017

%E a(29)-a(31) from _Robert Price_, Jul 26 2018