A288821 - OEIS

%I #13 Jun 06 2024 23:23:46

%S 3,6,9,11,12,25,47,166,222,234,352,407,515,646,1161,2475,4329,7191,

%T 12894,16007,25819,67579,88457,117135

%N Numbers k such that 10^k - 401 is prime.

%C For k > 2, numbers k such that k-3 occurrences of the digit 9 followed by the digits 599 is prime (see Example section).

%C a(25) > 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 9w599</a>.

%e 6 is in this sequence because 10^6 - 401 = 999599 is prime.

%e Initial terms and associated primes:

%e a(1) = 3, 599;

%e a(2) = 6, 999599;

%e a(3) = 9, 999999599;

%e a(4) = 11, 99999999599;

%e a(5) = 12, 999999999599; etc.

%t Select[Range[3, 100000], PrimeQ[10^# - 401] &]

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Jun 17 2017

%E a(24) from _Robert Price_, Jan 19 2018