A129904 Find the first two terms in A003215, say A003215(i) and A003215(j), that are divisible by a number in A016921 not 1, say by k = A016921(m). Then i + j + 1 = k and k is added to the sequence.

7, 13, 19, 31, 37, 43, 49, 61, 67, 73, 79, 91, 97, 103, 109, 127, 133, 139, 151, 157, 163, 169, 181, 193, 199, 211, 217, 223, 229, 241, 247, 259, 271, 277, 283, 301, 307, 313, 331, 337, 343, 349, 361, 367, 373, 379, 397, 403, 409, 421, 427, 433, 439, 457, 463

Offset: 1

Author

Mats Granvik, Jun 04 2007

Keywords

• nonn

Comments

Is this A004611 without the 1? - R. J. Mathar, Jul 16 2020

a(n) = A004611(n+1) for (at least) n <= 10^6. - Hugo Pfoertner, Oct 17 2020

Examples

			A003215(1) = 7 is divisible by A016921(1) = 7, A003215(5) = 91 is divisible by A016921(1) = 7 and 5+1+1=7, so 7 is a member.
		

Crossrefs

Cf. A003215, A016921, A004611.

Programs

Maple

isA129904 := proc(k)
    local i,j ;
    if modp(k,6) = 1 and k> 1 then
        for i from 0 to k-1 do
            j := k-1-i ;
            if modp(A003215(i),k) =0 and modp(A003215(j),k) =0 then
                return true;
            end if;
        end do:
        false ;
    else
        false;
    end if;
end proc:
for k from 1 to 400 do
    if isA129904(k) then
        printf("%d,",k) ;
    end if;
end do:

PARI

isA129904(k)={my(a003215(n)=3*n*(n+1)+1);if(k%6!=1||k<=1,0, for(i=0,k-1,my(j=k-1-i); if(a003215(i)%k==0&&a003215(j)%k==0, return(1))));0};
for(k=1,500,if(isA129904(k),print1(k,", "))) \\ Hugo Pfoertner, Oct 17 2020

Extensions

Extended by R. J. Mathar, Dec 16 2016