A282505 - OEIS

%I #14 May 25 2024 14:28:39

%S 1,2,3,4,5,6,12,32,63,116,154,221,267,468,605,749,1911,7241,7406,7797,

%T 9428,11094,43917,44127,58384,131223,181127

%N Numbers k such that (5*10^k - 29)/3 is prime.

%C For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 6 followed by the digits 57 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 16w57</a>.

%e 3 is in this sequence because (5*10^3 - 29)/3 = 1657 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 7;

%e a(2) = 2, 157;

%e a(3) = 3, 1657;

%e a(4) = 4, 16657;

%e a(5) = 5, 166657; etc.

%t Select[Range[1, 100000], PrimeQ[(5*10^# - 29)/3] &]

%o (PARI) isok(k) = isprime((5*10^k - 29)/3); \\ _Michel Marcus_, Mar 06 2018

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Feb 16 2017

%E a(26)-a(27) from _Robert Price_, Mar 05 2018