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Numbers k such that (182*10^k + 1)/3 is prime.
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%I #15 Jun 10 2024 23:36:37

%S 0,1,2,6,8,12,15,19,30,31,110,175,358,456,475,1359,1741,2061,6062,

%T 7568,10027,10732,27761,52018,75456,133543,136291,203048

%N Numbers k such that (182*10^k + 1)/3 is prime.

%C For k > 1, numbers k such that the digits 60 followed by k-1 occurrences of the digit 6 followed by the digit 7 is prime (see Example section).

%C a(29) > 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 606w7</a>.

%e 2 is in this sequence because (182*10^2 + 1)/3 = 6067 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 61;

%e a(2) = 1, 607;

%e a(3) = 2, 6067;

%e a(4) = 6, 60666667;

%e a(5) = 8, 6066666667; etc.

%t Select[Range[0, 100000], PrimeQ[(182*10^# + 1)/3] &]

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

%K nonn,more,hard

%O 1,3

%A _Robert Price_, Feb 13 2017

%E a(26)-a(27) from _Robert Price_, Feb 27 2020

%E a(28) from _Robert Price_, Oct 25 2023