A276546 - OEIS

%I #19 Jun 08 2024 15:41:05

%S 1,3,6,15,19,34,37,88,141,216,239,246,288,365,429,762,1879,2309,9555,

%T 19843,28348,45058,62879,86963,90669,148020,148601,199003,289877

%N Numbers k such that (151*10^k - 1)/3 is prime.

%C Numbers k such that the digits 50 followed by k occurrences of the digit 3 is prime (see Example section).

%C a(30) > 3*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 503w</a>.

%e 3 is in this sequence because (151*10^3 - 1)/3 = 50333 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 503;

%e a(2) = 3, 50333;

%e a(3) = 6, 50333333;

%e a(4) = 15, 50333333333333333;

%e a(5) = 19, 503333333333333333333; etc.

%t Select[Range[0, 100000], PrimeQ[(151*10^# - 1)/3] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Apr 09 2017

%E a(26)-a(28) from _Robert Price_, Mar 17 2020

%E a(29) from _Robert Price_, Oct 25 2023