A280449 - OEIS

%I #17 May 26 2024 14:29:00

%S 2,3,5,6,8,11,15,25,38,54,101,105,158,295,303,389,482,558,693,1965,

%T 3503,9818,13255,30351,51285,54767,57384,88808,109645,174301,187062

%N Numbers k such that (2*10^k - 71)/3 is prime.

%C For k > 1, numbers k such that the number consisting of k-2 occurrences of the digit 6 followed by the digits 43 is prime (see Example section).

%C a(32) > 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 6w43</a>.

%e 5 is in this sequence because (2*10^5 - 71) / 3 = 66643 is prime.

%e Initial terms and associated primes:

%e a(1) = 2, 43;

%e a(2) = 3, 643;

%e a(3) = 5, 66643;

%e a(4) = 6, 666643;

%e a(5) = 8, 66666643; etc.

%t Select[Range[2, 100000], PrimeQ[(2*10^# - 71) / 3] &]

%o (PARI) is(n)=isprime((2*10^n - 71)/3) \\ _Charles R Greathouse IV_, Jan 03 2017

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Jan 03 2017

%E a(29) - a(31) from _Robert Price_, Dec 31 2017