login
Numbers k such that (871*10^k - 7)/9 is prime.
0

%I #13 May 18 2024 11:32:35

%S 1,2,7,26,28,31,38,47,59,226,233,656,752,1073,1808,3646,4252,5246,

%T 24686,37952,59599

%N Numbers k such that (871*10^k - 7)/9 is prime.

%C Numbers k such that the digits 96 followed by k occurrences of the digit 7 is prime (see Example section).

%C a(22) > 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 967w</a>.

%e 2 is in this sequence because (871*10^2 - 7)/9 = 9677 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 967;

%e a(2) = 2, 9677;

%e a(3) = 7, 967777777;

%e a(4) = 26, 9677777777777777777777777777;

%e a(5) = 28, 967777777777777777777777777777; etc.

%t Select[Range[0, 100000], PrimeQ[(871*10^# - 7)/9] &]

%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Nov 06 2017