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Numbers k such that 3*10^k - 97 is prime.
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%I #21 Jun 09 2024 22:01:38

%S 3,5,6,7,28,42,45,59,69,179,271,293,621,851,2632,2764,5811,6813,7974,

%T 17015,30449,32760,43939,85227,87573,93179,122345,156435,174665,

%U 177373,292344

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

%C For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 9 followed by the digits 03 is prime (see Example section).

%C a(32) > 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 29w03</a>.

%e 5 is in this sequence because 3*10^5 - 97 = 299903 is prime.

%e Initial terms and associated primes:

%e a(1) = 3, 2903;

%e a(2) = 5, 299903;

%e a(3) = 6, 2999903;

%e a(4) = 7; 29999903;

%e a(5) = 28, 29999999999999999999999999903; etc.

%t Select[Range[2, 100000], PrimeQ[3*10^# - 97] &]

%o (PARI) isok(n) = isprime(3*10^n - 97); \\ _Michel Marcus_, Aug 07 2017

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Aug 06 2017

%E a(27)-a(30) from _Robert Price_, Jul 18 2018

%E a(31) from _Robert Price_, Jun 17 2023