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Search: id:A103266
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| A103266 |
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Minimal number of squares needed to sum to Fibonacci(n+1). |
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+0
3
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| 1, 2, 3, 2, 2, 2, 3, 2, 4, 2, 1, 2, 2, 2, 3, 2, 3, 2, 3, 2, 4, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 2, 4, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 4, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 2, 4, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 2, 4, 2, 4, 2, 2, 2, 3, 2, 3, 2, 3, 2, 4, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 2, 4
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Since every positive integer is the sum of four squares, no term is greater than 4. Also, since any positive integer not of the form 4^k(8m+7) is the sum 3 or fewer squares, the next occurrences of a(n)=4 are at n = 45, 57, 69, 81, 83, 93,.... - John W. Layman (layman(AT)math.vt.edu), Mar 30 2005
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REFERENCES
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Hardy and Wright, An Introduction to the Theory of Numbers, Fourth Ed., Oxford, Section 20.10.
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FORMULA
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a(n) = A002828(A000045(n+1)).
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EXAMPLE
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Fibonacci(10+1) = 89 = 25+64, so a(10)=2.
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CROSSREFS
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Cf. A000045, A002828.
Sequence in context: A078832 A086410 A147561 this_sequence A072814 A145390 A128049
Adjacent sequences: A103263 A103264 A103265 this_sequence A103267 A103268 A103269
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KEYWORD
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nonn
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AUTHOR
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Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it), Mar 20 2005
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EXTENSIONS
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Corrected and extended by John W. Layman (layman(AT)math.vt.edu), Mar 30 2005
Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), May 16 2005
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