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A275410 Numbers k such that (493*10^k - 7)/9 is prime.

%I A275410 #20 Jun 09 2024 16:14:34
%S A275410 1,2,5,7,8,14,19,22,23,31,62,65,79,178,356,401,517,557,1040,2248,6718,
%T A275410 10730,15079,24938,36241,58486,69340
%N A275410 Numbers k such that (493*10^k - 7)/9 is prime.
%C A275410 Numbers k such that the digits 54 followed by k occurrences of the digit 7 is prime (see Example section).
%C A275410 a(28) > 10^5.
%H A275410 Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H A275410 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 547w</a>.
%e A275410 5 is in this sequence because (493*10^5-7)/9 = 5477777 is prime.
%e A275410 Initial terms and associated primes:
%e A275410 a(1) = 1, 547;
%e A275410 a(2) = 2, 5477;
%e A275410 a(3) = 5, 5477777;
%e A275410 a(4) = 7, 547777777;
%e A275410 a(5) = 8, 5477777777, etc.
%t A275410 Select[Range[0, 100000], PrimeQ[(493*10^#-7)/9] &]
%o A275410 (Magma) [n: n in [0..500] | IsPrime((493*10^n-7) div 9)]; // _Vincenzo Librandi_, Jul 27 2016
%o A275410 (PARI) is(n)=ispseudoprime((493*10^n-7)/9) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y A275410 Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K A275410 nonn,more
%O A275410 1,2
%A A275410 _Robert Price_, Jul 26 2016