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Numbers k such that (4*10^k + 137)/3 is prime.
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%I #15 May 26 2024 23:00:15

%S 0,1,2,5,8,13,18,31,42,43,48,53,210,792,1324,1868,2544,5609,10210,

%T 10514,11232,14731,36583,50060,128510,198268

%N Numbers k such that (4*10^k + 137)/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 79 is prime (see Example section).

%C a(27) > 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 13w79</a>.

%e 5 is in this sequence because (4*10^5 + 137)/3 = 179 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 47;

%e a(2) = 1, 59;

%e a(3) = 2, 179;

%e a(4) = 5, 133379;

%e a(5) = 8, 133333379; etc.

%t Select[Range[0, 100000], PrimeQ[(4*10^# + 137)/3] &]

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

%K nonn,more,hard

%O 1,3

%A _Robert Price_, Jul 11 2017

%E a(25)-a(26) from _Robert Price_, Mar 21 2018