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Numbers k such that (4*10^k + 197)/3 is prime.
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%I #16 Jun 08 2024 08:55:35

%S 0,1,2,3,4,9,12,36,42,46,75,97,153,174,204,1078,1306,1380,2096,2401,

%T 3393,9547,16650,41404,64014

%N Numbers k such that (4*10^k + 197)/3 is prime.

%C For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 3 followed by the digits 99 is prime (see Example section).

%C a(26) > 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 13w99</a>.

%e 3 is in this sequence because (4*10^3 + 197)/3 = 1399 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 67;

%e a(2) = 1, 79;

%e a(3) = 2, 199;

%e a(4) = 3, 1399;

%e a(5) = 4, 13399; etc.

%t Select[Range[0, 100000], PrimeQ[(4*10^# + 197)/3] &]

%o (PARI) isok(n) = isprime((4*10^n + 197)/3); \\ _Indranil Ghosh_, Mar 09 2017

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

%K nonn,more,hard

%O 1,3

%A _Robert Price_, Mar 07 2017