A131320 2*n - maximal value arising in the sequence S(n) representing the digital sum analog base n of the Fibonacci recurrence.

1, 2, 3, 3, 5, 3, 3, 3, 5, 3, 3, 11, 7, 3, 3, 6, 9, 3, 3, 8, 9, 10, 11, 3, 9, 3, 3, 3, 15, 26, 8, 13, 10, 12, 3, 11, 19, 3, 23, 13, 13, 3, 21, 3, 23, 10, 3, 3, 9, 3, 3, 16, 17, 3, 3, 23, 17, 19, 29, 22, 11, 3, 17, 10, 25, 3, 22, 3, 35, 30, 11, 29, 57, 3, 3, 17, 65, 16, 13, 20, 21, 3, 3

Offset

1,2

Comments

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

a(n)=3 arises infinitely often; lim inf a(n)=3 for n-->oo.

Links

Table of n, a(n) for n=1..83.

Formula

a(n)=2n-A131319(n).

a(Lucas(2n))=3 where Lucas(n)=A000032(n).

Example

a(3)=3, since the digital sum analog base 3 of the Fibonacci sequence is 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 which implies 2*3-3=3. a(9)=5, because the pattern here is {2,3,5,8,13,13,10,7,9,8,9,9} (see A010076) where the maximal value is 13 and so 2*9-13=5.

Crossrefs

Cf. A000032, A000045, A000032, A131318, A131320.

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

Sequence in context: A063256 A229703 A348883 * A020483 A119912 A076368

Adjacent sequences: A131317 A131318 A131319 * A131321 A131322 A131323

Keyword

nonn,base

Author

Hieronymus Fischer, Jul 08 2007

Status

approved