A281929 - OEIS

%I #67 Jun 10 2024 23:36:53

%S 1,2,3,8,10,12,67,188,192,228,363,372,658,1748,1866,2539,7897,10399,

%T 10519,12872,14796,16773,24736,30456,46425,57316,65572,75338

%N Numbers k such that (19*10^k + 119)/3 is prime.

%C For k > 1, numbers k such that the digit 6 followed by k-2 occurrences of the digit 3 followed by the digits 73 is prime (see Example section).

%C a(29) > 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 63w73</a>.

%e 3 is in this sequence because (19*10^3 + 119)/3 = 6373 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 103;

%e a(2) = 2, 673;

%e a(3) = 3, 6373;

%e a(4) = 8, 633333373;

%e a(5) = 10, 63333333373; etc.

%t Select[Range[0, 100000], PrimeQ[(19*10^# + 119)/3] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Feb 11 2017