%I A000797 M5033 N2172
%S A000797 17,27,33,52,73,82,83,103,107,137,153,162,217,219,227,237,247,258,
%T A000797 268,271,282,283,302,303,313,358,383,432,437,443,447,502,548,557,
%U A000797 558,647,662,667,709,713,718,722,842,863,898,953,1007,1117,1118
%N A000797 Numbers that are not the sum of 4 tetrahedral numbers.
%C A000797 It is an open problem of long standing ("Pollock's Conjecture") to show 
               that this sequence is finite.
%C A000797 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 A000797 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000797 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000797 L. E. Dickson, History of the Theory of Numbers, Vol. II, Diophantine 
               Analysis. AMS Chelsea Publishing, Providence, Rhode Island, 1999, 
               p. 22.
%D A000797 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 A000797 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 A000797 S. S. Skiena, The Algorithm Design Manual, Springer-Verlag, 1998, pp. 
               43-45 and 135-136.
%H A000797 Jud McCranie and David W. Wilson, <a href="b000797.txt">The 241 known 
               terms</a>
%H A000797 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PollocksConjecture.html">Pollock's Conjecture</a>
%H A000797 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               TetrahedralNumber.html">Tetrahedral Number</a>
%Y A000797 Cf. A000292 (tetrahedral numbers), A104246.
%Y A000797 Sequence in context: A140150 A166658 A033702 this_sequence A147202 A146776 
               A147218
%Y A000797 Adjacent sequences: A000794 A000795 A000796 this_sequence A000798 A000799 
               A000800
%K A000797 nonn,fini
%O A000797 1,1
%A A000797 N. J. A. Sloane (njas(AT)research.att.com).
%E A000797 Entry revised Feb 25 2005