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A118487
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Least number of squares that add up to Lucas numbers L(n).
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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(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.
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REFERENCES
| Hardy and Wright, An Introduction to the Theory of Numbers, Fourth Ed., Oxford, Section 20.10.
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FORMULA
| a(n) = A002828(A000032(n)).
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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.
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CROSSREFS
| Cf. A000032, A000045, A002828, A103266.
Sequence in context: A088445 A020653 A094522 * A091420 A020952 A079554
Adjacent sequences: A118484 A118485 A118486 * A118488 A118489 A118490
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), May 16 2006
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