A191112 First occurrence of the n-th odd prime in A190911.

1, 3, 12, 42, 165, 3000, 2142, 39270, 838695, 2185092, 194467182, 649154415, 33547795512, 40753286805, 24563658547425, 1364238471026340, 2297427262231332, 1662166966658270160, 783186317937632697, 404695317060455732220, 162293533192142440777455, 634357227813958501290435

Offset: 1

Author

Nathaniel Johnston, May 26 2011

Keywords

• nonn

Crossrefs

Cf. A190911.

Programs

Maple

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:

PARI

A190911(n)=n*=n+3;forprime(p=3,,if(n%p,return(p)))
{my(v=[0],t=3,p=5);
print1("1, 3");
forprime(q=7,1000,
    u=vector(#v);
    for(i=1,#u,
        u[i]=lift(chinese(Mod(v[i],t),Mod( 0,p)));
        v[i]=lift(chinese(Mod(v[i],t),Mod(-3,p)))
    );
    v=vecsort(concat(u,v));
    for(j=2,#v,
        if(A190911(v[j])==q,
            print1(", "v[j]);
            break
        )
    );
    t*=p;
    p=q
)} \\ Charles R Greathouse IV, Oct 09 2011

Formula

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

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

Extensions

a(11)-a(22) from Charles R Greathouse IV, Oct 09 2011