login
Numbers k such that (13*10^k + 191)/3 is prime.
0

%I #13 May 27 2024 07:16:25

%S 1,3,4,18,28,40,45,49,78,165,312,469,855,899,1137,1314,1410,3832,

%T 10518,24163,28792,36947,56909,58103,59797,139782

%N Numbers k such that (13*10^k + 191)/3 is prime.

%C For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 3 followed by the digits 97 is prime (see Example section).

%C a(27) > 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 43w97</a>.

%e 3 is in this sequence because (13*10^3 + 191)/3 = 4397 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 107;

%e a(2) = 3, 4397;

%e a(3) = 4, 43397;

%e a(4) = 18; 4333333333333333397;

%e a(5) = 28, 43333333333333333333333333397; etc.

%t Select[Range[0, 100000], PrimeQ[(13*10^# + 191)/3] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Aug 14 2017

%E a(26) from _Robert Price_, Nov 28 2018