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A196000 Numbers k such that 90*k + 19 is prime.

%I A196000 #24 May 10 2019 21:45:55
%S A196000 0,1,2,4,8,9,10,11,14,16,17,22,23,24,25,28,30,34,35,36,39,41,43,46,48,
%T A196000 50,53,55,56,60,63,64,65,69,74,77,78,79,80,81,83,85,86,91,93,98,99,
%U A196000 101,102,107,108,109,111,112,115,116
%N A196000 Numbers k such that 90*k + 19 is prime.
%C A196000 A142322 is a digital root 1 and last digit 9 preserving sequence.
%H A196000 Ivan Neretin, <a href="/A196000/b196000.txt">Table of n, a(n) for n = 1..10000</a>
%F A196000 a(n) = (A142322(n) - 19)/90.
%p A196000 A142322 := proc(n)
%p A196000         option remember;
%p A196000         if n = 1 then
%p A196000                 19 ;
%p A196000         else
%p A196000                 a := nextprime(procname(n-1)) ;
%p A196000                 while (a mod 45) <> 19 do
%p A196000                         a := nextprime(a) ;
%p A196000                 end do;
%p A196000                 return a;
%p A196000         end if;
%p A196000 end proc:
%p A196000 A196000 := proc(n)
%p A196000         (A142322(n)-19)/90 ;
%p A196000 end proc:
%p A196000 seq(A196000(n),n=1..80) ; # _R. J. Mathar_, Oct 31 2011
%t A196000 Select[Range[0, 120], PrimeQ[90 # + 19] &] (* _Ivan Neretin_, Apr 27 2017 *)
%o A196000 (PARI) is(n)=isprime(90*n+19) \\ _Charles R Greathouse IV_, Apr 25 2016
%Y A196000 Cf. A195953, A181732, A198382.
%K A196000 nonn,easy
%O A196000 1,3
%A A196000 _J. W. Helkenberg_, Oct 27 2011