A293827 - OEIS

%I #12 May 27 2024 02:17:55

%S 2,3,11,14,15,20,23,24,39,104,374,428,698,1436,1521,1800,1809,3848,

%T 4796,46314,49182,82044,96137,141836

%N Numbers k such that (41*10^k - 59)/9 is prime.

%C For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 5 followed by the digits 49 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 45w49</a>.

%e 3 is in this sequence because (41*10^3 - 59)/9 = 4549 is prime.

%e Initial terms and associated primes:

%e a(1) = 2, 449;

%e a(2) = 3, 4549;

%e a(3) = 11, 455555555549;

%e a(4) = 14, 455555555555549;

%e a(5) = 15, 4555555555555549; etc.

%t Select[Range[1, 100000], PrimeQ[(41*10^# - 59)/9] &]

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Oct 16 2017

%E a(24) from _Robert Price_, Oct 27 2018