|
%I #12 May 02 2024 04:27:39
%S 1,3,7,12,15,21,85,177,204,477,487,1686,2179,2815,2892,3466,7308,
%T 17883,25431,69048,89169,126441
%N Numbers k such that (43*10^k + 47)/9 is prime.
%C For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 7 followed by the digits 83 is prime (see Example section).
%C a(23) > 2*10^5.
%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/prime_difficulty.txt">Search for 47w83</a>.
%e 3 is in this sequence because (43*10^3 + 47)/9 = 4783 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 53;
%e a(2) = 3, 4783;
%e a(3) = 7, 47777783;
%e a(4) = 12, 4777777777783;
%e a(5) = 15, 4777777777777783; etc.
%t Select[Range[0, 100000], PrimeQ[(43*10^# + 47)/9] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,2
%A _Robert Price_, Dec 04 2017
%E a(22) from _Robert Price_, Dec 01 2018
|
