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A275287 Numbers k such that (26*10^k - 107)/9 is prime.

%I A275287 #15 May 02 2024 04:25:43
%S A275287 1,2,5,7,13,23,25,44,110,157,751,853,964,1135,2588,2602,2807,2888,
%T A275287 3272,4046,4798,16720,21410,22285,25888,34586,51764
%N A275287 Numbers k such that (26*10^k - 107)/9 is prime.
%C A275287 For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 8 followed by the digits 77 is prime (see Example section).
%C A275287 a(28) > 10^5.
%H A275287 Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H A275287 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 28w77</a>.
%e A275287 5 is in this sequence because (26*10^5 - 107)/9 = 288877 is prime.
%e A275287 Initial terms and associated primes:
%e A275287 a(1) = 1, 17;
%e A275287 a(2) = 2, 277;
%e A275287 a(3) = 5, 288877;
%e A275287 a(4) = 7, 28888877;
%e A275287 a(5) = 13, 28888888888877, etc.
%t A275287 Select[Range[0, 100000], PrimeQ[(26*10^# - 107)/9] &]
%o A275287 (PARI) lista(nn) = for(n=1, nn, if(ispseudoprime((26*10^n-107)/9), print1(n, ", "))); \\ _Altug Alkan_, Jul 22 2016
%Y A275287 Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K A275287 nonn,more
%O A275287 1,2
%A A275287 _Robert Price_, Jul 21 2016