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%I #17 May 25 2024 17:38:47
%S 1,2,4,5,11,28,34,35,36,49,65,90,126,1878,2089,3266,3818,6485,7710,
%T 8539,20603,34764,51283,176964,258494
%N Numbers k such that (23*10^k - 47)/3 is prime.
%C For k > 1, numbers k such that the digit 7 followed by k-2 occurrences of the digit 6 followed by the digits 51 is prime (see Example section).
%C a(26) > 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 76w51</a>.
%e 4 is in this sequence because (23*10^4 - 47)/3 = 76651 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 61;
%e a(2) = 2, 751;
%e a(3) = 4, 76651;
%e a(4) = 5, 766651;
%e a(5) = 11, 766666666651; etc.
%t Select[Range[1, 100000], PrimeQ[(23*10^# - 47)/3] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,2
%A _Robert Price_, Oct 04 2017
%E a(24) from _Robert Price_, Sep 22 2019
%E a(25) from _Robert Price_, Oct 25 2023