A281990 - OEIS

%I #18 Jun 10 2024 00:14:28

%S 1,4,16,25,27,39,109,117,720,989,1451,1477,1522,2242,2657,2694,2929,

%T 5927,7589,7844,9990,19475,43896,44304,95134,128343,129487

%N Numbers k such that (199*10^k - 7)/3 is prime.

%C For k > 1, numbers k such that the digits 66 followed by k-1 occurrences of the digit 3 followed by the digit 1 is prime (see Example section).

%C a(28) > 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 663w1</a>.

%e 4 is in this sequence because (199*10^4 - 7)/3 = 663331 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 661;

%e a(2) = 4, 663331;

%e a(3) = 16, 663333333333333331;

%e a(4) = 25, 663333333333333333333333331;

%e a(5) = 27, 66333333333333333333333333331; etc.

%t Select[Range[0, 100000], PrimeQ[(199*10^# - 7)/3] &]

%o (PARI) isok(k) = isprime((199*10^k - 7)/3); \\ _Michel Marcus_, Feb 04 2017

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Feb 04 2017

%E a(26)-a(27) from _Robert Price_, May 21 2020