|
| |
|
|
A104246
|
|
Minimal number of tetrahedral numbers needed to sum to n.
|
|
19
| |
|
|
1, 2, 3, 1, 2, 3, 4, 2, 3, 1, 2, 3, 4, 2, 3, 4, 5, 3, 4, 1, 2, 3, 4, 2, 3, 4, 5, 3, 4, 2, 3, 4, 5, 3, 1, 2, 3, 4, 2, 2, 3, 4, 3, 3, 2, 3, 4, 4, 3, 3, 4, 5, 4, 4, 2, 1, 2, 3, 3, 2, 3, 4, 4, 3, 3, 2, 3, 4, 4, 2, 3, 4, 5, 3, 3, 2, 3, 4, 4, 3, 4, 5, 5, 1, 2, 3, 4, 2, 3, 3, 2, 3, 4, 2, 3, 3, 4, 3, 4, 4, 3, 4
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| According to Dickson, Pollock conjectures that a(n) <= 5 for all n. Watson shows that a(n) <= 8 for all n, and Salzer and Levine show that a(n) <= 5 for n <= 452479659. - N. J. A. Sloane, Jul 15 2011
|
|
|
REFERENCES
| Dickson, L. E., History of the Theory of Numbers, Vol. 2: Diophantine Analysis. New York: Dover, 1952, see p. 13.
Pollock, F., On the Extension of the Principle of Fermat's Theorem of the Polygonal Numbers to the Higher Orders of Series Whose Ultimate Differences Are Constant. With a New Theorem Proposed, Applicable to All the Orders, Abs. Papers Commun. Roy. Soc. London 5, 922-924, 1843-1850.
Salzer, H. E. and Levine, N., Table of Integers Not Exceeding 1000000 that are Not Expressible as the Sum of Four Tetrahedral Numbers, Math. Comp. 12, 141-144, 1958.
Salzer, H. E. and Levine, N., 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.
|
|
|
LINKS
| N. J. A. Sloane, Transforms
Eric Weisstein's World of Mathematics, Tetrahedral Number
|
|
|
MAPLE
| tet:=[seq((n^3-n)/6, n=1..20)];
LAGRANGE(tet, 8, 120); # the LAGRANGE transform of a sequence is defined in A193101 - N. J. A. Sloane, Jul 15 2011
|
|
|
CROSSREFS
| Cf. A000292 (tetrahedral numbers), A000797 (numbers that need 5 tetrahedral numbers).
See also A102795-A102806, A102855-A102858. A104246, A193101, A193105.
Sequence in context: A098066 A096436 A053610 * A007720 A129968 A027615
Adjacent sequences: A104243 A104244 A104245 * A104247 A104248 A104249
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Eric Weisstein (eric(AT)weisstein.com), Feb 26, 2005
|
|
|
EXTENSIONS
| Edited by N. J. A. Sloane, Jul 15 2011
|
| |
|
|
