A294375 - OEIS

%I #11 May 19 2024 21:55:33

%S 0,1,2,3,6,7,8,12,17,272,315,405,560,728,919,1578,1608,4736,7751,

%T 18332,22787,50005,69265,91032,92591,148071,168181

%N Numbers k such that (16*10^k + 41)/3 is prime.

%C For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 3 followed by the digits 47 is prime (see Example section).

%C a(28) > 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 53w47</a>.

%e 2 is in this sequence because (16*10^2 + 41)/3 = 547 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 19;

%e a(2) = 1, 67;

%e a(3) = 2, 547;

%e a(4) = 3, 5347;

%e a(5) = 6, 5333347; etc.

%t Select[Range[0, 100000], PrimeQ[(16*10^# + 41)/3] &]

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

%K nonn,more,hard

%O 1,3

%A _Robert Price_, Oct 29 2017

%E a(26)-a(27) from _Robert Price_, Mar 13 2019