login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A035336 a(n) = 2*floor(n*phi) + n - 1, where phi = (1+sqrt(5))/2. 32
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. - 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

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

J. H. Conway and N. J. A. Sloane, Notes on the Para-Fibonacci and related sequences

C. Kimberling, Complementary equations and Wythoff Sequences, JIS 11 (2008) 08.3.3

C. Kimberling and K. B. Stolarsky, Slow Beatty sequences, devious convergence, and partitional divergence, Amer. Math. Monthly, 123 (No. 2, 2016), 267-273.

N. J. A. Sloane, Classic Sequences

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

a(n) = 2*A003622(n) - (n - 1) = A003623(n) - 1. - Franklin T. Adams-Watters, Jun 30 2009

A005713(a(n)) = 0. - Reinhard Zumkeller, Dec 30 2011

a(n) = A089910(n) - 2. - Bob Selcoe, Sep 21 2014

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 *)

Array[2 Floor[# GoldenRatio] + # - 1 &, 60] (* Robert G. Wilson v, Dec 12 2017 *)

PROG

(Haskell)

import Data.List (elemIndices)

a035336 n = a035336_list !! (n-1)

a035336_list = elemIndices 0 a005713_list

-- Reinhard Zumkeller, Dec 30 2011

(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

def a(n): return 2*floor(n*phi) + n - 1 # Indranil Ghosh, Jun 10 2017

CROSSREFS

Cf. A022342, A066096.

Cf. A139764, A089910, A194584.

Let A = A000201, B = A001950. Then AA = A003622, AB = A003623, BA = A035336, BB = A101864.

Sequence in context: A190447 A190375 A066097 * A246128 A226830 A059316

Adjacent sequences:  A035333 A035334 A035335 * A035337 A035338 A035339

KEYWORD

nonn

AUTHOR

N. J. A. Sloane and J. H. Conway

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 16 00:50 EDT 2018. Contains 316252 sequences. (Running on oeis4.)