A014368 a(n) = bc, where n = C(b,2)+C(c,1), b>c>=0.

20, 21, 30, 31, 32, 40, 41, 42, 43, 50, 51, 52, 53, 54, 60, 61, 62, 63, 64, 65, 70, 71, 72, 73, 74, 75, 76, 80, 81, 82, 83, 84, 85, 86, 87, 90, 91, 92, 93, 94, 95, 96, 97, 98, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 1110, 120, 121, 122, 123

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• base

Comments

The definition means: write n as the highest possible triangular number plus some nonnegative rest (so b is one plus the index of the greedy inverse of n in A000217), and concatenate the two decimal expansions of b and the rest. - R. J. Mathar, May 25 2023

References

• W. Bruns and J. Herzog, Cohen-Macaulay Rings, Cambridge, 1993, p. 158.

Programs

Maple

invA000217 := proc(n)
    local i;
    for i from 1 do
        if binomial(i+1,2) > n then
            return i;
        end if;
    end do:
end proc:
A014368 := proc(n)
    local b,c;
    b := invA000217(n) ;
    c := n-binomial(b,2) ;
    digcatL([b,c]) ;
end proc:
seq(A014368(n),n=1..70) ; # R. J. Mathar, May 25 2023