A131319 Maximal value arising in the sequence S(n) representing the digital sum analog base n of the Fibonacci recurrence.

1, 2, 3, 5, 5, 9, 11, 13, 13, 17, 19, 13, 19, 25, 27, 26, 25, 33, 35, 32, 33, 34, 35, 45, 41, 49, 51, 53, 43, 34, 54, 51, 56, 56, 67, 61, 55, 73, 55, 67, 69, 81, 65, 85, 67, 82, 91, 93, 89, 97, 99, 88, 89, 105, 107, 89, 97, 97, 89, 98, 111, 121, 109, 118, 105, 129, 112

Offset

1,2

Comments

The respective period lengths of S(n) are given by A001175(n-1) (which is the Pisano period to n-1) for n>=2.

The inequality a(n)<=2n-3 holds for n>2.

a(n)=2n-3 infinitely often; lim sup a(n)/n=2 for n-->oo.

Links

Table of n, a(n) for n=1..67.

Formula

For n=Lucas(2m)=A000032(2m) with m>0, we have a(n)=2n-3.

a(n)=2n-A131320(n).

Example

a(3)=3, since the digital sum analog base 3 of the Fibonacci sequence is S(3)=0,1,1,2,3,3,2,3,3,... where the pattern {2,3,3} is the periodic part (see A131294) and so has a maximal value of 3.
a(9)=13 because the pattern base 9 is {2,3,5,8,13,13,10,7,9,8,9,9} (see A010076) where the maximal value is 13.

Crossrefs

Cf. A000032, A000045, A131318, A131320.

See A010074, A010075, A010076, A010077, A131294, A131295, A131296, A131297 for the definition of the digital sum analog of the Fibonacci recurrence(in different bases).

Sequence in context: A360072 A139127 A239143 * A108962 A091608 A317081

Adjacent sequences: A131316 A131317 A131318 * A131320 A131321 A131322

Keyword

nonn,base

Author

Hieronymus Fischer, Jul 08 2007

Status

approved