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 A000797 Numbers that are not the sum of 4 tetrahedral numbers. (Formerly M5033 N2172) 2

%I M5033 N2172

%S 17,27,33,52,73,82,83,103,107,137,153,162,217,219,227,237,247,258,268,

%T 271,282,283,302,303,313,358,383,432,437,443,447,502,548,557,558,647,

%U 662,667,709,713,718,722,842,863,898,953,1007,1117,1118

%N Numbers that are not the sum of 4 tetrahedral numbers.

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

%C 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.

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

%D 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.

%D 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.

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

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

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

%H Jud McCranie and David W. Wilson, <a href="/A000797/b000797.txt">The 241 known terms</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PollocksConjecture.html">Pollock's Conjecture</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TetrahedralNumber.html">Tetrahedral Number</a>

%Y Cf. A000292 (tetrahedral numbers), A104246.

%K nonn,fini

%O 1,1

%A _N. J. A. Sloane_.

%E Entry revised Feb 25 2005

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