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Numbers k such that 97*10^k - 3 is prime.
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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