A193106 Minimal number of terms of A005826 needed to sum to n.

1, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 2, 3, 4, 1, 2, 3, 3, 4, 5, 2, 3, 4, 4, 5, 6, 3, 4, 1, 2, 3, 4, 4, 5, 2, 3, 4, 5, 5, 6, 3, 4, 5, 2, 3, 4, 4, 5, 1, 2, 3, 4, 5, 6, 2, 3, 4, 2, 3, 4, 3, 4, 5, 2, 3, 4, 4, 5, 6, 3, 4, 5, 3, 4, 5, 1, 2, 2, 3, 4, 5, 2, 3, 3, 4, 5, 3, 3, 4, 4, 2, 3, 3, 4, 5, 5, 3, 2, 3, 4, 5, 4, 4, 3, 2, 3, 3, 4, 5, 4, 1, 2, 3, 4, 5, 4, 2, 3, 4, 3

Offset: 1

Author

N. J. A. Sloane, Jul 15 2011

Keywords

• nonn

Comments

Watson showed that a(n) <= 8 for all n.

It is likely that a(n) <= 6 for all n (see A193107).

Links

• H. E. Salzer and N. Levine, Proof that every integer <= 452,479,659 is a sum of five numbers of the form Q_x = (x^3+5x)/6, x>= 0, Math. Comp., (1968), 191-192.
• G. L. Watson, Sums of eight values of a cubic polynomial, J. London Math. Soc., 27 (1952), 217-224.

Crossrefs

Cf. A005826, A193107.

Programs

Maple

t1:=[seq((n^3-7*n)/6, n=3..20)];
LAGRANGE(t1, 8 120); # the LAGRANGE transform of a sequence is defined in A193101 - N. J. A. Sloane, Jul 15 2011