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A000797
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Numbers that are not the sum of 4 tetrahedral numbers.
(Formerly M5033 N2172)
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8
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17, 27, 33, 52, 73, 82, 83, 103, 107, 137, 153, 162, 217, 219, 227, 237, 247, 258, 268, 271, 282, 283, 302, 303, 313, 358, 383, 432, 437, 443, 447, 502, 548, 557, 558, 647, 662, 667, 709, 713, 718, 722, 842, 863, 898, 953, 1007, 1117, 1118
(list;
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listen;
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OFFSET
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1,1
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COMMENTS
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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.
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REFERENCES
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L. E. Dickson, History of the Theory of Numbers, Vol. II, Diophantine Analysis. AMS Chelsea Publishing, Providence, Rhode Island, 1999, p. 22.
S. S. Skiena, The Algorithm Design Manual, Springer-Verlag, 1998, pp. 43-45 and 135-136.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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CROSSREFS
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KEYWORD
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nonn,fini
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AUTHOR
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EXTENSIONS
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Entry revised Feb 25 2005
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STATUS
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approved
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