A281903 - OEIS

%I #17 May 25 2024 19:34:32

%S 0,1,3,4,10,16,18,19,33,54,75,95,268,407,539,547,661,1445,1559,2634,

%T 3316,7047,10299,10911,19528,29603,38668

%N Numbers k such that 6*10^k + 37 is prime.

%C For k > 1, numbers k such that the digit 6 followed by k-2 occurrences of the digit 0 followed by the digits 37 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 60w37</a>.

%e 3 is in this sequence because 6*10^3 + 37 = 6037 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 43;

%e a(2) = 1, 97;

%e a(3) = 3, 6037;

%e a(4) = 4, 60037;

%e a(5) = 10, 60000000037; etc.

%t Select[Range[0, 100000], PrimeQ[6*10^# + 37] &]

%o (PARI) isok(k) = isprime(6*10^k + 37); \\ _Michel Marcus_, Dec 10 2018

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

%K nonn,more,hard

%O 1,3

%A _Robert Price_, Feb 01 2017