A282140 - OEIS

%I #11 Jun 09 2024 18:05:32

%S 1,3,6,7,9,10,12,24,39,135,258,382,660,900,1306,1528,3658,3937,5157,

%T 7006,7936,10956,15396,45808,198403

%N Numbers k such that (49*10^k + 311)/9 is prime.

%C For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 4 followed by the digits 79 is prime (see Example section).

%C a(26) > 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 54w79</a>.

%e 3 is in this sequence because (49*10^3 + 311)/9 = 5479 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 89;

%e a(2) = 3, 5479;

%e a(3) = 6, 5444479;

%e a(4) = 7, 54444479;

%e a(5) = 9, 5444444479; etc.

%t Select[Range[0, 100000], PrimeQ[(49*10^# + 311)/9] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Feb 06 2017

%E a(25) from _Robert Price_, Jun 13 2019