A294125 - OEIS

%I #13 May 25 2024 13:55:10

%S 1,16,22,26,29,55,83,110,128,176,187,566,1150,1405,3515,7763,14530,

%T 18398,26035,42166,85897

%N Numbers k such that (412*10^k - 7)/9 is prime.

%C For k > 1, numbers k such that the digits 45 followed by k occurrences of the digit 7 is prime (see Example section).

%C a(22) > 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 457w</a>.

%e 1 is in this sequence because (412*10^1 - 7)/9 = 457 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 457;

%e a(2) = 16, 457777777777777777;

%e a(3) = 22, 457777777777777777777777;

%e a(4) = 26, 4577777777777777777777777777;

%e a(5) = 29, 4577777777777777777777777777777; etc.

%t Select[Range[0, 100000], PrimeQ[(412*10^# - 7)/9] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Oct 23 2017