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

Author

Parthasarathy Nambi, Apr 11 2007

Keywords

• nonn
• base

Comments

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A000045, A072354.

Programs

Mathematica

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 *)

Formula

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

Extensions

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