cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A004437 Numbers that are not the sum of 4 distinct squares.

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%I A004437 #27 Jan 01 2016 16:47:31
%S A004437 1,2,3,4,5,6,7,8,9,10,11,12,13,15,16,17,18,19,20,22,23,24,25,27,28,31,
%T A004437 32,33,34,36,37,40,43,44,47,48,52,55,58,60,64,67,68,72,73,76,80,82,88,
%U A004437 92,96,97,100,103,108,112
%N A004437 Numbers that are not the sum of 4 distinct squares.
%C A004437 It follows from the formula that there are infinitely many integers that cannot be partitioned into a sum of four distinct squares of nonnegative integers and infinitely many that can. Furthermore, the largest odd number that has no such partition is 103, and thereafter the terms satisfy the thirty-first order recurrence relation a(n) = 4a(n-31). - _Ant King_, Nov 02 2010
%H A004437 Gordon Pall, <a href="http://www.jstor.org/stable/2301257">On Sums of Squares</a>, The American Mathematical Monthly, Vol. 40, No. 1, (January 1933), pp. 10-18. [From _Ant King_, Nov 02 2010]
%H A004437 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F A004437 Let k>=0. Then the only integers that cannot be partitioned into a sum of four distinct squares of nonnegative integers are 4^k * N3, where N3 = (N1 union N2), and N1 and N2 are defined by N1 = {1,3,5,7,9,11,13,15,17,19,23,25,27,31,33,37,43,47,55,67,73,97,103} and N2 = {2,6,10,18,22,34,58,82}, respectively. - _Ant King_, Nov 02 2010
%t A004437 data = Reduce[ w^2 + x^2 + y^2 + z^2 == # && 0 <= w < x < y < z < #, {w, x, y, z}, Integers] & /@ Range[112]; DeleteCases[ Table[If[Head[data[[k]]] === Symbol, k, 0], {k, 1, Length[data]}], 0] (* _Ant King_, Nov 02 2010 *)
%Y A004437 Cf. A001944 (complement).
%K A004437 nonn
%O A004437 1,2
%A A004437 _N. J. A. Sloane_