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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.
5

%I #17 Jan 04 2018 03:42:50

%S 7,41,465,2732,3005,20648,48125,94396,129299,282931,789281,835050,

%T 1241217,1292143,1521647,1603655,2756953,4847702,5128447,6242598

%N 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.

%C a(21) > 10^7. - _Donovan Johnson_, Sep 29 2010

%D 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.

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

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

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

%K nice,nonn

%O 1,1

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

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

%E a(13)-a(16) from _Donovan Johnson_, Jun 21 2010

%E a(17)-a(20) from _Donovan Johnson_, Sep 29 2010