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Numbers k such that (28*10^k + 191)/3 is prime.
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%I #20 May 26 2024 15:03:44

%S 0,1,2,3,5,6,9,10,33,49,92,109,548,757,814,1289,1460,1644,2782,6355,

%T 8028,9276,9366,9765,12002,12089,14491,16180,29102,30989,151682,

%U 183403,190105,253210

%N Numbers k such that (28*10^k + 191)/3 is prime.

%C For k > 1, numbers k such that the digit 9 followed by k-2 occurrences of the digit 3 followed by the digits 97 is prime (see Example section).

%C a(35) > 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 93w97</a>.

%e 3 is in this sequence because (28*10^3 + 191)/3 = 9397 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 73;

%e a(2) = 1, 157:

%e a(3) = 2, 997;

%e a(4) = 3, 9397;

%e a(5) = 5, 933397, etc.

%t Select[Range[0, 100000], PrimeQ[(28*10^# + 191)/3] &]

%o (PARI) is(n)=ispseudoprime((28*10^n + 191)/3) \\ _Charles R Greathouse IV_, Jun 13 2017

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

%K nonn,more

%O 1,3

%A _Robert Price_, May 13 2016

%E a(31)-a(33) from _Robert Price_, Feb 27 2020

%E a(34) from _Robert Price_, Jul 12 2023