login
Numbers k such that (29*10^k + 673)/9 is prime.
0

%I #12 May 25 2024 13:55:07

%S 1,2,4,7,14,19,20,22,29,40,64,169,173,1513,2357,3193,4198,11864,18182,

%T 19576,31175,38030,57967,122996

%N Numbers k such that (29*10^k + 673)/9 is prime.

%C For k > 1, numbers k such that the digit 3 followed by k-2 occurrences of the digit 2 followed by the digits 97 is prime (see Example section).

%C a(25) > 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 32w97</a>.

%e 2 is in this sequence because (29*10^2 + 673)/9 = 397 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 107;

%e a(2) = 2, 397;

%e a(3) = 4, 32297;

%e a(4) = 7, 32222297;

%e a(5) = 14, 322222222222297; etc.

%t Select[Range[0, 100000], PrimeQ[(29*10^# + 673)/9] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Oct 16 2017

%E a(24) from _Robert Price_, Dec 07 2018