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Numbers k such that (16*10^k + 197) / 3 is prime.
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%I #25 May 25 2024 14:34:33

%S 0,2,3,5,8,10,111,114,456,1158,1241,1462,1736,1827,2523,2812,3305,

%T 5392,5897,6174,13683,17088,23771,28448,127259,142058,164122

%N Numbers k such that (16*10^k + 197) / 3 is prime.

%C For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 3 followed by the digits 99 is prime (see Example section).

%C a(28) > 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 53w99</a>.

%e 3 is in this sequence because (16*10^3 + 197) / 3 = 5399 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 71;

%e a(2) = 2, 599;

%e a(3) = 3, 5399;

%e a(4) = 5, 533399;

%e a(5) = 8, 533333399; etc.

%t Select[Range[0, 100000], PrimeQ[(16*10^# + 197) / 3] &]

%o (PARI) is(n)=ispseudoprime((16*10^n + 197)/3) \\ _Charles R Greathouse IV_, Jun 13 2017

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Dec 28 2016

%E a(25)-a(27) from _Robert Price_, Apr 03 2019