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Numbers k such that (16*10^k + 77)/3 is prime.
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%I #15 May 25 2024 19:13:19

%S 0,1,4,11,12,24,33,42,52,58,87,114,143,169,227,292,544,1341,1498,5011,

%T 7295,14958,15577,103127,107140,118852,122871

%N Numbers k such that (16*10^k + 77)/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 59 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 53w59</a>.

%e 4 is in this sequence because (16*10^4 + 77)/3 = 53359 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 31;

%e a(2) = 1, 79;

%e a(3) = 4, 53359;

%e a(4) = 11, 533333333359;

%e a(5) = 12, 5333333333359; etc.

%t Select[Range[0, 100000], PrimeQ[(16*10^# + 77)/3] &]

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

%K nonn,more,hard

%O 1,3

%A _Robert Price_, Apr 23 2017

%E a(24)-a(27) from _Robert Price_, Mar 10 2019