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A201816 Numbers k such that 90*k + 13 is prime.

%I A201816 #21 Sep 08 2022 08:46:01
%S A201816 0,1,2,3,4,5,7,8,9,12,16,17,19,22,23,30,31,35,36,37,38,40,42,46,47,49,
%T A201816 50,51,53,58,59,60,61,63,66,67,68,74,75,80,82,84,86,88,92,95,99,100,
%U A201816 101,103,105,107,108,112,114,116,119,121,122,123,124,126,127
%N A201816 Numbers k such that 90*k + 13 is prime.
%C A201816 Looking at the format 90*k+13 modulo 9 and modulo 10 we see that all entries of A142318 have digital root 4 and last digit 3. (Reverting the process is an application of the Chinese remainder theorem.)
%H A201816 Vincenzo Librandi, <a href="/A201816/b201816.txt">Table of n, a(n) for n = 1..10000</a>
%p A201816 a:= proc(n) option remember; local k;
%p A201816        for k from 1+ `if`(n=1, -1, a(n-1))
%p A201816        while not isprime(90*k+13) do od; k
%p A201816     end:
%p A201816 seq(a(n), n=1..100);  # _Alois P. Heinz_, Dec 06 2011
%t A201816 Select[Range[0,4000],PrimeQ[90 #+13]&] (* _Vincenzo Librandi_, Dec 12 2011 *)
%o A201816 (Magma) [n: n in [0..200] | IsPrime(90*n+13)]; // _Vincenzo Librandi_, Dec 12 2011
%o A201816 (PARI) is(n)=isprime(90*n+13) \\ _Charles R Greathouse IV_, Jul 12 2016
%Y A201816 Cf. A181732, A198382, A195993, A196000, A196007, A201739, A201734, A201804.
%K A201816 nonn,easy
%O A201816 1,3
%A A201816 _J. W. Helkenberg_, Dec 05 2011