A072354 -id:A072354 - cp's OEIS frontend

A128823 a(n) is the sum of all n-digit Fibonacci numbers.

20, 212, 2351, 15127, 178707, 1981891, 21979508, 141422324, 1670731762, 18528699171, 205486422643, 2278879348244, 14662949395604, 173224810531570, 1921092587268915, 21305243270489635, 236278768562654900

Offset: 1

Parthasarathy Nambi, Apr 11 2007

The minimum, average and maximum of a(n)/10^n are approximately equal to 1.38197968245, 1.87028385088 & 2.38195747810, respectively, 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, May 26 2007
Observation: There are approximately twice as many odd terms as even ones.

			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.

Robert G. Wilson v, Table of n, a(n) for n = 1..100
C. Valente, PlanetMath.org, List of Fibonacci Numbers
Wikipedia, Fibonacci Numbers.

Cf. A000045, A072354.

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, May 26 2007 *)

a(n) = A000045(A072354(n+1)+1) - A000045(A072354(n)+1). - Christopher Hohl, May 27 2019

More terms from Robert G. Wilson v, May 26 2007

A164018 The index values of the smallest and the largest n-digit Fibonacci numbers.

Original entry on oeis.org

0, 6, 7, 11, 12, 16, 17, 20, 21, 25, 26, 30, 31, 35, 36, 39, 40, 44, 45, 49, 50, 54, 55, 59, 60, 63, 64, 68, 69, 73, 74, 78, 79, 83, 84, 87, 88, 92, 93, 97, 98, 102, 103, 106, 107, 111, 112, 116, 117, 121, 122, 126, 127, 130, 131, 135, 136, 140, 141, 145

Offset: 0

Parthasarathy Nambi, Aug 07 2009

= A072354 + A072353 [From Parthasarathy Nambi, Sep 14 2009]

			The index value of the smallest ten digit Fibonacci number is 45. The index value of the largest ten digit Fibonacci number is 49.

Harvey P. Dale, Table of n, a(n) for n = 0..999

Cf. A000045

Drop[Flatten[{#-1,#}&/@Flatten[Table[Position[IntegerLength[Fibonacci[ Range[250]]],n,1,1],{n,50}]]],{2}](* Harvey P. Dale, Jun 04 2018 *)

More terms from Harvey P. Dale, Jun 04 2018

cp's OEIS Frontend

A128823 a(n) is the sum of all n-digit Fibonacci numbers.

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