|
|
A035336
|
|
a(n) = 2*floor(n*phi) + n - 1, where phi = (1+sqrt(5))/2.
|
|
33
|
|
|
2, 7, 10, 15, 20, 23, 28, 31, 36, 41, 44, 49, 54, 57, 62, 65, 70, 75, 78, 83, 86, 91, 96, 99, 104, 109, 112, 117, 120, 125, 130, 133, 138, 143, 146, 151, 154, 159, 164, 167, 172, 175, 180, 185, 188, 193, 198, 201, 206, 209, 214, 219, 222, 227, 230, 235, 240
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Second column of Wythoff array.
These are the numbers in A022342 that are not images of another value of the same sequence if it is given offset 0. - Michele Dondi (bik.mido(AT)tiscalenet.it), Dec 30 2001
Also, positions of 2's in A139764, the smallest term in Zeckendorf representation of n. - John W. Layman, Aug 25 2011
Numbers k for which the Zeckendorf representation A014417(k) ends with 0, 1, 0.
The asymptotic density of this sequence is sqrt(5)-2. (End)
|
|
LINKS
|
|
|
FORMULA
|
a(n) = B(A(n)), with A(k)=A000201(k) and B(k)=A001950(k) (Wythoff BA-numbers).
a(n) = A(n) + A(A(n)), with A(A(n))=A003622(n) (Wythoff AA-numbers).
Equals A022342(A003622(n)+1). - Michele Dondi (bik.mido(AT)tiscalenet.it), Dec 30 2001, sequence reference updated by Peter Munn, Nov 23 2017
|
|
MAPLE
|
Digits := 100: t := (1+sqrt(5))/2; [ seq(2*floor((n+1)*t)+n, n=0..80) ];
|
|
MATHEMATICA
|
Table[2*Floor[n*(1 + Sqrt[5])/2] + n - 1, {n, 50}] (* Wesley Ivan Hurt, Nov 21 2017 *)
|
|
PROG
|
(Haskell)
import Data.List (elemIndices)
a035336 n = a035336_list !! (n-1)
a035336_list = elemIndices 0 a005713_list
(Magma) [2*Floor(n*(1+Sqrt(5))/2)+n-1: n in [1..80]]; // Vincenzo Librandi, Nov 19 2016
(Python)
from sympy import floor
from mpmath import phi
(Python)
from math import isqrt
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|