A287210 - OEIS

%I #12 Jun 06 2024 23:23:42

%S 0,1,2,4,11,14,15,16,18,21,28,44,55,286,304,494,970,1611,2051,2756,

%T 6452,16758,29291,98413,113954,197702

%N Numbers k such that 78*10^k - 7 is prime.

%C For k > 1, numbers k such that the digits 77 followed by k-1 occurrences of the digit 9 followed by the digit 3 is prime (see Example section).

%C a(27) > 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 779w3</a>.

%e 2 is in this sequence because 78*10^2 - 7 = 7793 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 71;

%e a(2) = 1, 773;

%e a(3) = 2, 7793;

%e a(4) = 4, 779993;

%e a(5) = 11, 7799999999993; etc.

%t Select[Range[0, 100000], PrimeQ[78*10^# - 7] &]

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

%K nonn,more,hard

%O 1,3

%A _Robert Price_, May 21 2017

%E a(25)-a(26) from _Robert Price_, Oct 08 2020