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A035105
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a(n) = LCM of Fibonacci sequence {F_1,...,F_n}.
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14
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1, 1, 2, 6, 30, 120, 1560, 10920, 185640, 2042040, 181741560, 1090449360, 254074700880, 7368166325520, 449458145856720, 21124532855265840, 33735878969859546480, 640981700427331383120, 2679944489486672512824720, 109877724068953573025813520
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OFFSET
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1,3
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LINKS
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Yuri V. Matiyasevich and Richard K. Guy, A new formula for Pi, The American Mathematical Monthly, Vol 93, No. 8 (1986), pp. 631-635.
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FORMULA
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log(a(n)) ~ 3*n^2*log(phi)/Pi^2, where phi is the golden ratio, or equivalently lim_{n->oo} sqrt(6*log(A003266(n))/log(a(n))) = Pi. - Amiram Eldar, Jan 30 2019
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MAPLE
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a:= proc(n) option remember; `if`(n=1, 1,
ilcm(a(n-1), combinat[fibonacci](n)))
end:
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MATHEMATICA
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a[ n_ ] := LCM@@Table[ Fibonacci[ k ], {k, 1, n} ]
With[{fibs=Fibonacci[Range[20]]}, Table[LCM@@Take[fibs, n], {n, Length[ fibs]}]] (* Harvey P. Dale, Apr 29 2019 *)
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PROG
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(Python)
from math import lcm
from sympy import fibonacci
def A035105(n): return lcm(*(fibonacci(i) for i in range(1, n+1))) # Chai Wah Wu, Jul 17 2022
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Fred Schwab (fschwab(AT)nrao.edu)
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STATUS
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approved
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