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%I #15 Jun 09 2024 22:16:17
%S 1,2,3,8,9,13,30,31,33,35,85,97,105,129,242,253,295,2810,2991,3479,
%T 7902,16867,21744,38687,51027,72522,84033,91205,161247,190295
%N Numbers k such that 97*10^k - 3 is prime.
%C For k > 0, numbers k such that the digits 96 followed by k-1 occurrences of the digit 9 followed by the digit 7 is prime (see Example section).
%C a(31) > 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 969w7</a>.
%e 3 is in this sequence because 97*10^3 - 3 = 96997 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 967;
%e a(2) = 2, 9697;
%e a(3) = 3, 96997;
%e a(4) = 8, 9699999997;
%e a(5) = 9, 96999999997; etc.
%t Select[Range[0, 100000], PrimeQ[97*10^# - 3] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,2
%A _Robert Price_, Jan 14 2017
%E a(29)-a(30) from _Robert Price_, May 26 2020