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A201817 Numbers k such that 90*k + 67 is prime.

%I A201817 #21 Sep 08 2022 08:46:01
%S A201817 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 A201817 57,61,62,63,64,66,69,70,72,73,76,77,79,83,85,90,94,96,98,100,101,103,
%U A201817 107,108,110,117,118,120,121,122,125,127,128,129,133,138,139
%N A201817 Numbers k such that 90*k + 67 is prime.
%C A201817 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 A201817 Vincenzo Librandi, <a href="/A201817/b201817.txt">Table of n, a(n) for n = 1..10000</a>
%p A201817 a:= proc(n) option remember; local k;
%p A201817        for k from 1+ `if`(n=1, -1, a(n-1))
%p A201817        while not isprime(90*k+67) do od; k
%p A201817     end:
%p A201817 seq(a(n), n=1..100);  # _Alois P. Heinz_, Dec 06 2011
%t A201817 Select[Range[0,4000],PrimeQ[90 #+67]&] (* _Vincenzo Librandi_, Dec 12 2011 *)
%o A201817 (Magma) [n: n in [0..200] | IsPrime(90*n+67)]; // _Vincenzo Librandi_, Dec 12 2011
%o A201817 (PARI) is(n)=isprime(90*n+67) \\ _Charles R Greathouse IV_, Feb 17 2017
%Y A201817 Cf. A181732, A198382, A195993, A196000, A196007, A201739, A201734, A201804, A201816.
%K A201817 nonn,easy
%O A201817 1,3
%A A201817 _J. W. Helkenberg_, Dec 05 2011