

A118487


Least number of squares that add up to Lucas numbers L(n).


1



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, 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, 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
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OFFSET

1,1


COMMENTS

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(n1) + F(n2), F(0) = 0, F(1) = 1, F(2) = 1, ... See also: A002828 Least number of squares that add up to n.


REFERENCES

Hardy and Wright, An Introduction to the Theory of Numbers, Fourth Ed., Oxford, Section 20.10.


LINKS



FORMULA



EXAMPLE

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.
a(20) = 4 because L(20) = 15127 = 74^2 + 73^2 + 59^2 + 29^2.
a(30) = 2 because L(30) = 1860498 = 1077^2 + 837^2.
a(100) = 4 because L(100) = 16930663951^2 + 16706810102^2 + 13499760391^2 + 6637953271^2.


CROSSREFS



KEYWORD

easy,nonn


AUTHOR



STATUS

approved



