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

Author

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

Keywords

• nice
• nonn

Comments

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

Examples

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

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.

Crossrefs

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

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