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Numbers k such that 98*10^k - 3 is prime.
0

%I #12 Jun 09 2024 22:01:42

%S 1,5,7,8,13,20,33,39,43,51,91,113,119,132,208,411,525,581,931,1552,

%T 4829,17537,40301,43429

%N Numbers k such that 98*10^k - 3 is prime.

%C For k > 0, numbers k such that the digits 97 followed by k-1 occurrences of the digit 9 followed by the digit 7 is prime (see Example section).

%C a(25) > 2*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 979w7</a>.

%e 5 is in this sequence because 98*10^5 - 3 = 9799997 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 977;

%e a(2) = 5, 9799997;

%e a(3) = 7, 979999997;

%e a(4) = 8, 9799999997;

%e a(5) = 13, 979999999999997; etc.

%t Select[Range[0, 100000], PrimeQ[98*10^# - 3] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Jun 05 2017