A131280 Sums of exactly 4 positive octahedral numbers A005900.

4, 9, 14, 19, 22, 24, 27, 32, 37, 40, 45, 47, 50, 52, 57, 58, 62, 63, 65, 70, 75, 76, 83, 88, 90, 93, 95, 98, 100, 101, 103, 106, 108, 111, 113, 116, 124, 126, 129, 131, 133, 136, 138, 141, 142, 149, 151, 154, 159, 164, 167, 172, 174, 176, 177, 179, 182, 185, 190

Offset

1,1

Comments

Pollock (1850) conjectured that every number is the sum of at most 7 octahedral numbers. Which octahedral numbers are themselves the sum of exactly 4 positive octahedral numbers? To begin with, Oc(3) = Oc(2) + Oc(2) + Oc(2) + Oc(1) = 6 + 6 + 6 + 1 = 19.

References

Dickson, L. E. History of the Theory of Numbers, Vol. 2: Diophantine Analysis. New York: Dover, 2005, cites the Pollock reference.

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.

Links

Table of n, a(n) for n=1..59.

Mathematica

With[{octs=Table[(2n^3+n)/3, {n, 10}]}, Take[Union[Total/@Tuples[octs, 4]], 60]] (* Harvey P. Dale, Nov 26 2013 *)

Crossrefs

Cf. A005900, A053676-A053678, A133330.

Sequence in context: A031474 A045203 A313082 * A313083 A313084 A313085

Adjacent sequences: A131277 A131278 A131279 * A131281 A131282 A131283

Keyword

easy,nonn

Author

Jonathan Vos Post, Oct 21 2007

Status

approved