A272830 - OEIS

%I #17 May 02 2024 04:27:25

%S 1,2,3,8,9,10,16,31,35,79,179,196,239,376,515,728,812,1154,2000,2379,

%T 2485,3523,3987,5221,5257,5739,17863,59127,106454,125894

%N Numbers k such that (8*10^k - 29)/3 is prime.

%C For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 6 followed by the digits 57 is prime (see Example section).

%C a(31) > 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 26w57</a>.

%e 3 is in this sequence because (8*10^3 - 29)/3 = 2657 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 17;

%e a(2) = 2, 257;

%e a(3) = 3, 2657;

%e a(4) = 8, 266666657;

%e a(5) = 9, 2666666657, etc.

%t Select[Range[0, 100000], PrimeQ[(8*10^# - 29)/3] &]

%o (PARI) is(n)=ispseudoprime((8*10^n-29)/3) \\ _Charles R Greathouse IV_, Jun 13 2017

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

%K nonn,more

%O 1,2

%A _Robert Price_, May 07 2016

%E a(29)-a(30) from _Robert Price_, Jul 03 2018