%I #17 May 26 2024 14:57:53

%S 0,1,2,4,13,19,39,62,76,79,109,184,222,265,370,626,670,679,763,1950,

%T 2174,3379,7369,9087,34990,47535,97970

%N Numbers k such that 42 * 10^k + 1 is prime.

%C For k > 0, numbers k such that the digits 42 followed by k - 1 occurrences of the digit 0 followed by the digit 1 is prime (see the Example section).

%C a(28) > 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 420w1</a>.

%e 4 is in this sequence because 42*10^4+1 = 420001 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 43;

%e a(2) = 1, 421;

%e a(3) = 2, 4201;

%e a(4) = 4, 420001;

%e a(5) = 13, 420000000000001, etc.

%t Select[Range[0, 100000], PrimeQ[42 * 10^# + 1] &]

%o (PARI) is(n)=ispseudoprime(42*10^n+1) \\ _Charles R Greathouse IV_, Jun 13 2017

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

%K nonn,more

%O 1,3

%A _Robert Price_, Aug 20 2016