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%I #25 Jan 17 2019 13:44:08
%S 2,4,5,8,11,25,35,270,401,613,635,768,1283,2941,3409,4266,4391,10744,
%T 22979,26766,27743,35514,59174,86906,99239,154494
%N Numbers k such that (10^k - 13)/3 is prime.
%C For k > 1, numbers such that k - 2 occurrences of the digit 3 followed by the digits 29 is prime (see Example section).
%C a(27) > 2 * 10^5. - Price
%C There are no odd multiples of 3 in this sequence. If k is an odd multiple of 3, then (10^k - 13)/3 is divisible by 7. The smallest even multiple of 3 in the sequence is 270. - _Alonso del Arte_, Dec 31 2017
%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/primedifficulty.txt">Search for 3w29.</a>
%e 4 is in this sequence because (10^4 - 13)/3 = 3329 is prime.
%e Here is a listing of the initial terms and associated primes:
%e a(1) = 2, 29;
%e a(2) = 4, 3329;
%e a(3) = 5, 33329;
%e a(4) = 8, 33333329;
%e a(5) = 11, 33333333329; etc.
%t Select[Range[2, 100000], PrimeQ[(10^# - 13)/3] &]
%o (PARI) isok(n) = isprime((10^n-13)/3); \\ _Altug Alkan_, Dec 31 2017
%Y Cf. A056707 (numerators of (10^k - 13)/3 that are prime for k negative), A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,1
%A _Robert Price_, Feb 21 2017
%E a(26) from _Robert Price_, Dec 31 2017
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