1,1

It is an open problem of long standing ("Pollock's Conjecture") to show that this sequence is finite.

More precisely, Salzer and Levine conjecture that every number is the sum of at most 5 tetrahedral numbers and in fact that there are exactly 241 numbers (the terms of this sequence) that require 5 tetrahedral numbers, the largest of which is 343867.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

L. E. Dickson, History of the Theory of Numbers, Vol. II, Diophantine Analysis. AMS Chelsea Publishing, Providence, Rhode Island, 1999, p. 22.

F. Pollock, 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, Proc. Roy. Soc. London, 5 (1851), 922-924.

H. E. Salzer and N. Levine, Table of integers not exceeding 10 00000 that are not expressible as the sum of four tetrahedral numbers, Math. Comp., 12 (1958), 141-144.

S. S. Skiena, The Algorithm Design Manual, Springer-Verlag, 1998, pp. 43-45 and 135-136.

Jud McCranie and David W. Wilson, The 241 known terms

Eric Weisstein's World of Mathematics, Pollock's Conjecture

Eric Weisstein's World of Mathematics, Tetrahedral Number

Cf. A000292 (tetrahedral numbers), A104246.

Sequence in context: A140150 A166658 A033702 this_sequence A147202 A146776 A147218

Adjacent sequences: A000794 A000795 A000796 this_sequence A000798 A000799 A000800

nonn,fini

N. J. A. Sloane (njas(AT)research.att.com).

Entry revised Feb 25 2005