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A276470 Numbers k such that (25*10^k + 167) / 3 is prime.

%I A276470 #36 May 26 2024 15:23:15
%S A276470 1,3,4,5,11,15,18,37,41,58,60,87,117,118,214,265,334,355,450,655,1695,
%T A276470 1734,2183,3913,25313,32865
%N A276470 Numbers k such that (25*10^k + 167) / 3 is prime.
%C A276470 For k > 1, numbers k such that the digit 8 followed by k-2 occurrences of the digit 3 followed by the digits 89 is prime (see Example section).
%C A276470 a(27) > 2*10^5.
%H A276470 Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H A276470 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 83w89</a>.
%e A276470 3 is in this sequence because (25*10^3 + 167) / 3 = 8389 is prime.
%e A276470 Initial terms and associated primes:
%e A276470 a(1) = 1, 139;
%e A276470 a(2) = 3, 8389
%e A276470 a(3) = 4, 83389;
%e A276470 a(4) = 5, 833389;
%e A276470 a(5) = 11, 833333333389, etc.
%t A276470 Select[Range[0, 100000], PrimeQ[(25*10^# + 167) / 3] &]
%o A276470 (Magma) [n: n in [0..400] |IsPrime((25*10^n + 167) div 3)]; // _Vincenzo Librandi_, Sep 13 2016
%o A276470 (PARI) is(n)=ispseudoprime((25*10^n + 167)/3) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y A276470 Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K A276470 nonn,more
%O A276470 1,2
%A A276470 _Robert Price_, Sep 12 2016