A191112 - OEIS

%I #13 Sep 26 2015 18:40:45

%S 1,3,12,42,165,3000,2142,39270,838695,2185092,194467182,649154415,

%T 33547795512,40753286805,24563658547425,1364238471026340,

%U 2297427262231332,1662166966658270160,783186317937632697,404695317060455732220,162293533192142440777455,634357227813958501290435

%N First occurrence of the n-th odd prime in A190911.

%F a(n) = 0 (mod 3) for n >= 2.

%F a(n) = 0 or 12 (mod 15) for n >= 3.

%p A190911 := proc(n) option remember: local k: for k from 3 by 2 do if(gcd(k,n)=1 and gcd(k,n+3)=1)then return k: fi: od: end: for n from 2 do p:=ithprime(n): for k from 1 do if(A190911(k)=p)then print(k): break: fi: od: od:

%o (PARI) A190911(n)=n*=n+3;forprime(p=3,,if(n%p,return(p)))

%o {my(v=[0],t=3,p=5);

%o print1("1, 3");

%o forprime(q=7,1000,

%o     u=vector(#v);

%o     for(i=1,#u,

%o         u[i]=lift(chinese(Mod(v[i],t),Mod( 0,p)));

%o         v[i]=lift(chinese(Mod(v[i],t),Mod(-3,p)))

%o     );

%o     v=vecsort(concat(u,v));

%o     for(j=2,#v,

%o         if(A190911(v[j])==q,

%o             print1(", "v[j]);

%o             break

%o         )

%o     );

%o     t*=p;

%o     p=q

%o )} \\ _Charles R Greathouse IV_, Oct 09 2011

%Y Cf. A190911.

%K nonn

%O 1,2

%A _Nathaniel Johnston_, May 26 2011

%E a(11)-a(22) from _Charles R Greathouse IV_, Oct 09 2011