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.
%I A118487 #3 Mar 30 2012 18:40:37 %S A118487 2,1,3,1,4,3,2,2,4,3,3,4,3,2,3,3,4,3,3,2,4,4,3,4,3,3,3,3,4,3,2,2,4,3, %T A118487 3,4,3,2,3,3,4,3,3,2,4,4,3,4,3,2,3,3,4,3,3,3,4,3,3,4,3,2,3,3,4,3,3,2, %U A118487 4,4,3,4,3,2,3,3,4,3,2,2,4,3,3,4,3,3,3,3,4,3,3,2,4,4,3,4,3,3,3,3,4 %N A118487 Least number of squares that add up to Lucas numbers L(n). %C A118487 By the "Four Squares theorem", a(n) <= 4. Any positive integer not of the form 4^k(8m+7) is the sum 3 or fewer squares. See also: A000032 Lucas numbers. See also: A103266 Minimal number of squares needed to sum to Fibonacci(n+1). See also: A000045 Fibonacci numbers: F(n) = F(n-1) + F(n-2), F(0) = 0, F(1) = 1, F(2) = 1, ... See also: A002828 Least number of squares that add up to n. %D A118487 Hardy and Wright, An Introduction to the Theory of Numbers, Fourth Ed., Oxford, Section 20.10. %F A118487 a(n) = A002828(A000032(n)). %e A118487 a(4) = 4 because L(4) = 7 = 2^2 + 2^2 + 1^1 + 1^1 is the minimum representation as sum of squares, in this case of 4 squares. %e A118487 a(20) = 4 because L(20) = 15127 = 74^2 + 73^2 + 59^2 + 29^2. %e A118487 a(30) = 2 because L(30) = 1860498 = 1077^2 + 837^2. %e A118487 a(100) = 4 because L(100) = 16930663951^2 + 16706810102^2 + 13499760391^2 + 6637953271^2. %Y A118487 Cf. A000032, A000045, A002828, A103266. %K A118487 easy,nonn %O A118487 1,1 %A A118487 _Jonathan Vos Post_, May 16 2006