A295328 - OEIS

%I #19 May 05 2024 00:21:11

%S 1,2,3,25,61,75,99,122,145,187,292,586,1328,2457,3410,4819,5986,6638,

%T 20855,28161,47647,49387,67499,72723

%N Numbers k such that 3*10^k + 67 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 67 is prime (see Example section).

%C a(25) > 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 30w67</a>.

%e 2 is in this sequence because 3*10^2 + 67 = 367 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 97;

%e a(2) = 2, 367;

%e a(3) = 3, 3067;

%e a(4) = 25, 30000000000000000000000067;  etc.

%t Select[Range[0, 100000], PrimeQ[3*10^# + 67] &]

%o (PARI) isok(k) = isprime(3*10^k + 67); \\ _Michel Marcus_, Nov 20 2017

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Nov 19 2017