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A273542 Numbers k such that (238*10^k - 1)/3 is prime.

%I A273542 #23 May 02 2024 04:24:43
%S A273542 0,2,3,4,6,10,12,38,40,47,59,76,131,154,227,404,762,782,987,993,3449,
%T A273542 5692,10086,11630,15135,26384,28233,33179,48352,103210,118265,145276,
%U A273542 151979,209715,210712
%N A273542 Numbers k such that (238*10^k - 1)/3 is prime.
%C A273542 For k > 1, numbers k such that the digits 79 followed by k occurrences of the digit 3 is prime (see Example section).
%C A273542 a(36) > 3*10^5.
%H A273542 Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H A273542 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 793w</a>.
%e A273542 3 is in this sequence because (238*10^3-1)/3 = 79333 is prime.
%e A273542 Initial terms and associated primes:
%e A273542 a(1) = 0, 79;
%e A273542 a(2) = 2, 7933;
%e A273542 a(3) = 3, 79333;
%e A273542 a(4) = 4, 793333;
%e A273542 a(5) = 6, 79333333, etc.
%t A273542 Select[Range[0, 100000], PrimeQ[(238*10^# - 1)/3] &]
%o A273542 (Magma) [n: n in [0..500] | IsPrime((238*10^n - 1) div 3)]; // _Vincenzo Librandi_, May 25 2016
%o A273542 (PARI) is(n)=ispseudoprime(238*10^n\3) \\ _Charles R Greathouse IV_, Jun 08 2016
%Y A273542 Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K A273542 nonn,more
%O A273542 1,2
%A A273542 _Robert Price_, May 24 2016
%E A273542 a(30)-a(33) from _Robert Price_, Apr 01 2020
%E A273542 a(34)-a(35) from _Robert Price_, Oct 26 2023