Search: id:A051952
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%I A051952
%S A051952 1,2,5,10,13,25,37,58,85,130
%N A051952 Numbers that are not a sum of 3 positive squares nor are of the form 
               4^a*(8b+7) and which are not multiples of 4.
%C A051952 The asymptotic eigenvalue spectrum of the Schroedinger equation for a 
               free particle in a box in three dimensions is known only (that is: 
               average level density and average degeneracy) if the a(n) are finite 
               series.
%D A051952 H.-P. Baltes, Peter K. J. Draxl and Eberhard R. Hilf, Quadratsummen und 
               gewisse Randwertprobleme der Mathematischen Physik, Journ. Reine 
               Angewandte Mathematik, Vol. 268/269, 1974, 410-417.
%D A051952 E. Grosswald, A. Calloway and J. Calloway, The representations of integers 
               by three positive squares, Proc. Amer. Math. Soc. 10 (1959), 451-455. 
               [Math. Rev. 21 #3376; E24-73 in Leveque's Reviews in Number Theory, 
               Vol. 2, p. 290]
%D A051952 E. R. Hilf, Diploma-thesis, Univ.Frankfurt,Germany, 1963 [available from 
               author]
%D A051952 E. R. Hilf, G. Suessmann, Surface Tension of nuclei according to the 
               Fermigas-Model; Physics Letters, Vol. 21, No. 6, p. 654-656, (1966)
%H A051952 H. P. Baltes and E. R. Hilf, <a href="http://www.physik.uni-oldenburg.de/
               Docs/THEO3/publications/metadocs/ebs.spectra.finite.systems.prep.html">
               Spectra of finite systems</a>; BI-Verlag
%H A051952 Eberhard R. Hilf, <a href="http://www.physik.uni-oldenburg.de/Docs/THEO3/
               publications/">Publications</a>
%H A051952 E. R. Hilf and H. P. Baltes, <a href="http://www.physik.uni-oldenburg.de/
               Docs/THEO3/publications/metadocs/ebs.130.and.cube.spectrum.html">
               130 and the cube spectrum, unpublished</a>
%H A051952 <a href="Sindx_Su.html#ssq">Index entries for sequences related to sums 
               of squares</a>
%e A051952 Consider a(3)=5: 1^2 +1^2 +1^2=3, too low; 1^2+1^2+2^2=6, too high. 4^1=4 
               too low; 4^2=16 too high; (8*0+7)=7 too low, (8*1+7)= 15 too high; 
               thus 5 is a member of this sequence.
%Y A051952 Sequence in context: A135467 A018571 A064233 this_sequence A103188 A064392 
               A018296
%Y A051952 Adjacent sequences: A051949 A051950 A051951 this_sequence A051953 A051954 
               A051955
%K A051952 hard,nonn,nice
%O A051952 1,2
%A A051952 Eberhard R. Hilf (hilf(AT)merlin.physik.uni-oldenburg.de), Dec 21 1999
%E A051952 It is not known whether 130 is the largest such number or if this is 
               the start of an infinite series.
%E A051952 Grosswald et al. reference from N. J. A. Sloane (njas(AT)research.att.com), 
               Jun 07 2000.

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