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A065885
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a(n)-1, a(n) and a(n)+1 form three consecutive integers that can be factored into Fibonacci numbers.
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2
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2, 3, 4, 5, 9, 25, 26, 64, 169, 441, 1156, 3025, 7921, 20736, 54289, 142129, 372100, 974169, 2550409, 6677056
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| In general it can be shown that F(n-1)F(n+1), F(n)^2, F(n-2)F(n+2) form three consecutive increasing integers when n is even and F(n-2)F(n+2), F(n)^2, F(n-1)F(n+1) for three consecutive increasing integers when n is odd. Thus the sequence is infinite.
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FORMULA
| Except for n = 1, 2, 4 and 7, a(n) is the square of a Fibonacci number.
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EXAMPLE
| 440 = 8*55, 441 = 21^2, 442 = 13*34, so 441 is a term of the sequence.
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CROSSREFS
| A065108, A000045, A007598
Sequence in context: A088817 A018896 A162374 * A177064 A092233 A115895
Adjacent sequences: A065882 A065883 A065884 * A065886 A065887 A065888
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KEYWORD
| nonn
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AUTHOR
| John W. Layman (layman(AT)math.vt.edu), Nov 28 2001
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