A201817 - OEIS

%I #21 Sep 08 2022 08:46:01

%S 0,1,3,6,8,9,10,13,14,17,19,20,23,29,30,31,33,35,36,42,44,47,50,51,56,

%T 57,61,62,63,64,66,69,70,72,73,76,77,79,83,85,90,94,96,98,100,101,103,

%U 107,108,110,117,118,120,121,122,125,127,128,129,133,138,139

%N Numbers k such that 90*k + 67 is prime.

%C Looking at the format 90*k + 67 modulo 9 and modulo 10 we see that all entries of A142323 have digital root 4 and last digit 7. (Reverting the process is an application of the Chinese remainder theorem.)

%H Vincenzo Librandi, <a href="/A201817/b201817.txt">Table of n, a(n) for n = 1..10000</a>

%p a:= proc(n) option remember; local k;

%p        for k from 1+ `if`(n=1, -1, a(n-1))

%p        while not isprime(90*k+67) do od; k

%p     end:

%p seq(a(n), n=1..100);  # _Alois P. Heinz_, Dec 06 2011

%t Select[Range[0,4000],PrimeQ[90 #+67]&] (* _Vincenzo Librandi_, Dec 12 2011 *)

%o (Magma) [n: n in [0..200] | IsPrime(90*n+67)]; // _Vincenzo Librandi_, Dec 12 2011

%o (PARI) is(n)=isprime(90*n+67) \\ _Charles R Greathouse IV_, Feb 17 2017

%Y Cf. A181732, A198382, A195993, A196000, A196007, A201739, A201734, A201804, A201816.

%K nonn,easy

%O 1,3

%A _J. W. Helkenberg_, Dec 05 2011