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Search: id:A128823
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| A128823 |
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a(n) = sum of all n-digit Fibonacci numbers. |
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+0
3
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| 20, 212, 2351, 15127, 178707, 1981891, 21979508, 141422324, 1670731762, 18528699171, 205486422643, 2278879348244, 14662949395604, 173224810531570, 1921092587268915, 21305243270489635, 236278768562654900
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The minimum, average and maximum of a(n)/10^n are approximately equal to 1.38197968245, 1.87028385088 & 2.38195747810, respectfully, for the first 30000 terms.
Observation: the minimum seems to be just over (5-sqrt(5))/2, the maximum seems to be just shy of (7-sqrt(5))/2; the average is not (6-sqrt(5))/2 but seems to be closer to (5-sqrt(11))/9. - Robert G. Wilson v.
Observation: There are approxiately twice as many odd entries as even ones.
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LINKS
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Robert G. Wilson v, Table of n, a(n) for n = 1..100
cvalente, PlanetMath.org, List of Fibonacci Numbers
Wikipedia, Fibonacci Numbers.
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EXAMPLE
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If n=1 then the sum of the Fibonacci numbers 1+1+2+3+5+8 = 20 which is the first term in the sequence.
If n=2 then the sum of the Fibonacci numbers 13+21+34+55+89 = 212 which is the second term in the sequence.
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MATHEMATICA
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f[n_] := Plus @@ Select[ Fibonacci /@ Range[ Floor[(n - 1)*Log[ GoldenRatio, 10] + 1], Floor[ n*Log[ GoldenRatio, 10] + 3]], Floor@ Log[10, # ] + 1 == n &]; Array[f, 18] (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A000045, A072354.
Sequence in context: A022585 A007744 A121204 this_sequence A141790 A125408 A140236
Adjacent sequences: A128820 A128821 A128822 this_sequence A128824 A128825 A128826
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KEYWORD
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nonn,base
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AUTHOR
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Parthasarathy Nambi (PachaNambi(AT)yahoo.com), Apr 11 2007
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), May 26 2007
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