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A276546 Numbers k such that (151*10^k - 1)/3 is prime.

%I A276546 #19 Jun 08 2024 15:41:05
%S A276546 1,3,6,15,19,34,37,88,141,216,239,246,288,365,429,762,1879,2309,9555,
%T A276546 19843,28348,45058,62879,86963,90669,148020,148601,199003,289877
%N A276546 Numbers k such that (151*10^k - 1)/3 is prime.
%C A276546 Numbers k such that the digits 50 followed by k occurrences of the digit 3 is prime (see Example section).
%C A276546 a(30) > 3*10^5.
%H A276546 Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H A276546 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 503w</a>.
%e A276546 3 is in this sequence because (151*10^3 - 1)/3 = 50333 is prime.
%e A276546 Initial terms and associated primes:
%e A276546 a(1) = 1, 503;
%e A276546 a(2) = 3, 50333;
%e A276546 a(3) = 6, 50333333;
%e A276546 a(4) = 15, 50333333333333333;
%e A276546 a(5) = 19, 503333333333333333333; etc.
%t A276546 Select[Range[0, 100000], PrimeQ[(151*10^# - 1)/3] &]
%Y A276546 Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K A276546 nonn,more,hard
%O A276546 1,2
%A A276546 _Robert Price_, Apr 09 2017
%E A276546 a(26)-a(28) from _Robert Price_, Mar 17 2020
%E A276546 a(29) from _Robert Price_, Oct 25 2023