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A214981 Number of terms in the greedy Lucas-and-Fibonacci representations of 1,2,...,n; partial sums of A214973. 4
1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 14, 16, 17, 19, 21, 23, 25, 26, 28, 30, 31, 33, 35, 37, 39, 41, 44, 46, 47, 49, 51, 53, 55, 56, 58, 60, 62, 64, 66, 69, 71, 73, 76, 79, 81, 84, 85, 87, 89, 91, 93, 95, 98, 100, 101, 103, 105, 107, 109, 111, 114, 116, 118, 121, 124 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For comparison with Zeckendorf (Fibonacci) representations, it is conjectured that the limit of A179180(n)/A214981(n) exists and is between 1.2 and 1.4.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000

Clark Kimberling, Lucas Representations of Positive Integers, J. Int. Seq., Vol. 23 (2020), Article 20.9.5.

EXAMPLE

The basis is B = (1,2,3,4,5,7,8,11,13,18,21,29,34,47,55,...), composed of Fibonacci numbers and Lucas numbers. Representations of positive integers using the greedy algorithm on B:

   n  repres.   # terms  a(n)

   1   1        1        1

   2   2        1        2

   3   3        1        3

   4   4        1        4

   5   5        1        5

   6   5+1      2        7

   7   7        1        8

   8   8        1        9

   9   8+1      2       11

  10   8+2      2       13

  27   21+5+1   3       44

MATHEMATICA

(See the program at A214973.)

CROSSREFS

Cf. A000032, A000045, A179180, A214973, A214977, A214979, A214980, A214981.

Sequence in context: A078448 A212289 A191840 * A322030 A326623 A210576

Adjacent sequences:  A214978 A214979 A214980 * A214982 A214983 A214984

KEYWORD

nonn

AUTHOR

Clark Kimberling, Oct 22 2012

EXTENSIONS

Edited by Clark Kimberling, Jun 13 2020

STATUS

approved

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Last modified May 15 16:02 EDT 2021. Contains 343920 sequences. (Running on oeis4.)