login
Numbers k such that (22*10^k + 161)/3 is prime.
0

%I #17 Jun 15 2024 17:52:58

%S 0,1,2,4,5,6,7,13,28,36,40,74,233,425,828,888,1970,2119,2338,2971,

%T 3030,14005,20190,29589,47034,47292,51457,64326,70259,90110,120828,

%U 122681

%N Numbers k such that (22*10^k + 161)/3 is prime.

%C For k > 1, numbers k such that the digit 7 followed by k-2 occurrences of the digit 3 followed by the digits 87 is prime (see Example section).

%C a(33) > 3*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 73w87</a>.

%e 4 is in this sequence because (22*10^4 + 161)/3 = 73387 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 61;

%e a(2) = 1, 127;

%e a(3) = 2, 787;

%e a(4) = 4, 73387;

%e a(5) = 5, 733387; etc.

%t Select[Range[0, 100000], PrimeQ[(22*10^# + 161)/3] &]

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

%K nonn,more,hard

%O 1,3

%A _Robert Price_, Feb 10 2017

%E a(31)-a(32) from _Robert Price_, May 04 2019