cp's OEIS Frontend

A004441 Numbers that are not the sum of 4 distinct nonzero squares.

%I A004441 #38 Jan 10 2025 09:47:17
%S A004441 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
%T A004441 27,28,29,31,32,33,34,35,36,37,38,40,41,42,43,44,45,47,48,49,52,53,55,
%U A004441 56,58,59,60,61,64,67,68
%N A004441 Numbers that are not the sum of 4 distinct nonzero squares.
%C A004441 It has been shown that 157 is the last odd number in this sequence. Beyond 157, the terms grow exponentially. - _T. D. Noe_, Apr 07 2007
%C A004441 Taking a(86) to a(120) as initial terms, A004441(n) satisfies the 35th-order recurrence relation u(n) = 4*u(n-35). - _Ant King_, Aug 13 2010
%H A004441 T. D. Noe, <a href="/A004441/b004441.txt">Table of n, a(n) for n = 1..1000</a> (using A004195 and A004196)
%H A004441 Paul T. Bateman, Adolf J. Hildebrand and George B. Purdy, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa67/aa6745.pdf">Sums of distinct squares</a>, Acta Arith. 67 (1994), 349-380.
%H A004441 H. D. Nguyen and D. Taggart, <a href="https://citeseerx.ist.psu.edu/pdf/8f2f36f22878c984775ed04368b8893879b99458">Mining the OEIS: Ten Experimental Conjectures</a>, 2013. [Mentions this sequence.]
%H A004441 <a href="/index/Rec#order_35">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4).
%H A004441 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%t A004441 data1=Reduce[w^2+x^2+y^2+z^2==# && 0<w<x<y<z<#,{w,x,y,z},Integers]&/@Range[1000];data2=If[Head[ # ]===And,1,Length[ # ]] &/@data1;DeleteCases[Table[If[data2[[k]]>0,0,k],{k,1,Length[data2]}],0] (* _Ant King_, Aug 13 2010 *)
%Y A004441 Cf. A004195, A004196, A004433 (complement).
%K A004441 nonn,easy
%O A004441 1,2
%A A004441 _N. J. A. Sloane_