A053676 Let Oc(n) = A005900(n) = n-th octahedral number. Consider all integer triples (i,j,k), j >= k > 0, with Oc(i) = Oc(j)+Oc(k), ordered by increasing i; sequence gives i values.

7, 41, 465, 2732, 3005, 20648, 48125, 94396, 129299, 282931, 789281, 835050, 1241217, 1292143, 1521647, 1603655, 2756953, 4847702, 5128447, 6242598

Offset

1,1

Comments

a(21) > 10^7. - Donovan Johnson, Sep 29 2010

References

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.

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

Links

Table of n, a(n) for n=1..20.

Example

Oc(7) = 231 = Oc(6) + Oc(5); Oc(41) = 45961 = Oc(40) + Oc(17); Oc(465) = 67029905 = Oc(454) + Oc(191)

Crossrefs

Cf. A005900, A053677 (j values), A053678 (k values).

Sequence in context: A146991 A377347 A356129 * A002701 A057006 A144747

Adjacent sequences: A053673 A053674 A053675 * A053677 A053678 A053679

Keyword

nice,nonn

Author

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Feb 16 2000

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), May 07 2001

a(13)-a(16) from Donovan Johnson, Jun 21 2010

a(17)-a(20) from Donovan Johnson, Sep 29 2010

Status

approved