login
Numbers k such that 4*10^k + 39 is prime.
0

%I #15 May 18 2024 11:34:11

%S 0,1,2,4,6,12,19,23,24,86,110,120,258,359,584,1144,2833,10346,13333,

%T 23238,29546,44356,59292

%N Numbers k such that 4*10^k + 39 is prime.

%C For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 0 followed by the digits 39 is prime (see Example section).

%C a(24) > 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 40w39</a>.

%e 2 is in this sequence because 4*10^2 + 39 = 439 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 43;

%e a(2) = 1, 79;

%e a(3) = 2, 439;

%e a(4) = 4, 40039;

%e a(5) = 6, 4000039; etc.

%t Select[Range[0, 100000], PrimeQ[4*10^# + 39] &]

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

%K nonn,more,hard

%O 1,3

%A _Robert Price_, Nov 10 2017