A293034 - OEIS

%I #12 May 25 2024 17:38:15

%S 1,5,12,17,21,23,25,29,109,168,195,327,417,461,1991,3512,3955,4239,

%T 6228,24317,91613,131457,152143,159381,162689

%N Numbers k such that (203*10^k + 1)/3 is prime.

%C For k > 0, numbers k such that the digits 67 followed by k-1 occurrences of the digit 6 followed by the digit 7 is prime (see Example section).

%C a(26) > 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 676w7</a>.

%e 5 is in this sequence because (203*10^5 + 1)/3 = 6766667 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 677;

%e a(2) = 5, 6766667;

%e a(3) = 12, 67666666666667;

%e a(4) = 17, 6766666666666666667;

%e a(5) = 21, 67666666666666666666667; etc.

%t Select[Range[0, 100000], PrimeQ[(203*10^# + 1)/3] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Sep 28 2017

%E a(22)-a(25) from _Robert Price_, Mar 22 2020