A024612 a(n) = number in position n when all i^2 - i*j + j^2, where 1 <= i < j are arranged in increasing order.

3, 7, 7, 12, 13, 13, 19, 19, 21, 21, 27, 28, 28, 31, 31, 37, 37, 39, 39, 43, 43, 48, 49, 49, 52, 52, 57, 57, 61, 61, 63, 63, 67, 67, 73, 73, 75, 76, 76, 79, 79, 84, 84, 91, 91, 91, 91, 93, 93, 97, 97, 103, 103, 108, 109, 109, 111, 111, 112, 112, 117, 117, 124, 124, 127, 127, 129, 129, 133

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Programs

Maple

A024612 := proc(n)
    local i,j,disc;
    # n=i^2+j^2-i*j = (j-i)^2+i*j, 1<=i=1 and i*j>=j and i^2+j^2-i*j >= 1+j max search radius
    for j from 2 to n-1 do
        # i=(j +- sqrt(4n-3j^2))/2
        disc := 4*n-3*j^2 ;
        if disc >= 0 then
            if issqr(disc) then
                i := (j+sqrt(disc))/2 ;
                if type(i,'integer') and i >= 1 and i 0 then
                    i := (j-sqrt(disc))/2 ;
                    if type(i,'integer') and i >= 1 and iA024612(t);
end do: # R. J. Mathar, Aug 21 2016