A282975 - OEIS

%I #15 May 25 2024 14:28:34

%S 0,1,6,13,18,28,40,45,50,70,101,210,248,298,1246,1340,1586,2466,6548,

%T 6713,7394,23904,32450,38171,39120,67816,108610,112400,129038

%N Numbers k such that (134*10^k + 7)/3 is prime.

%C For k > 0, numbers k such that the digits 44 followed by k-1 occurrences of the digit 6 followed by the digit 9 is prime (see Example section).

%C a(30) > 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 446w9</a>.

%e 1 is in this sequence because (134*10^1 + 7)/3 = 449 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 47;

%e a(2) = 1, 449;

%e a(3) = 6, 44666669;

%e a(4) = 13, 446666666666669;

%e a(5) = 18, 44666666666666666669; etc.

%t Select[Range[0, 100000], PrimeQ[(134*10^# + 7)/3] &]

%o (PARI) isok(k) = isprime((134*10^k + 7)/3); \\ _Michel Marcus_, Feb 26 2017

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

%K nonn,more,hard

%O 1,3

%A _Robert Price_, Feb 26 2017

%E a(27)-a(29) from _Robert Price_, Feb 05 2020