A294914 - OEIS

%I #15 May 18 2024 11:33:48

%S 4,7,10,27,40,43,55,61,63,117,259,417,427,561,568,889,1335,26625,

%T 36613,45261,47205

%N Numbers k such that (14*10^k - 131)/9 is prime.

%C For k > 1, numbers k such that the digit 6 followed by k-2 occurrences of the digit 5 followed by the digits 47 is prime (see Example section).

%C a(22) > 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 15w41</a>.

%e 4 is in this sequence because (14*10^4 - 131)/9 = 15541 is prime.

%e Initial terms and associated primes:

%e a(1) = 4, 15541;

%e a(2) = 7, 15555541;

%e a(3) = 10, 15555555541;

%e a(4) = 27, 1555555555555555555555555541;

%e a(5) = 40, 15555555555555555555555555555555555555541; etc.

%t Select[Range[1, 100000], PrimeQ[(14*10^# - 131)/9] &]

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Nov 10 2017