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

%I

%S 2,7,10,15,20,23,28,31,36,41,44,49,54,57,62,65,70,75,78,83,86,91,96,

%T 99,104,109,112,117,120,125,130,133,138,143,146,151,154,159,164,167,

%U 172,175,180,185,188,193,198,201,206,209,214,219,222,227,230,235,240

%N a(n) = 2*floor(n*phi) + n - 1, where phi = (1+sqrt(5))/2.

%C Second column of Wythoff array.

%C 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

%C Also, positions of 2's in A139764, the smallest term in Zeckendorf representation of n. - _John W. Layman_, Aug 25 2011

%H Reinhard Zumkeller, <a href="/A035336/b035336.txt">Table of n, a(n) for n = 1..10000</a>

%H J. H. Conway and N. J. A. Sloane, <a href="/A019586/a019586.pdf">Notes on the Para-Fibonacci and related sequences</a>

%H C. Kimberling, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL11/Kimberling/kimberling719a.html">Complementary equations and Wythoff Sequences</a>, JIS 11 (2008) 08.3.3

%H C. Kimberling and K. B. Stolarsky, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.123.3.267">Slow Beatty sequences, devious convergence, and partitional divergence</a>, Amer. Math. Monthly, 123 (No. 2, 2016), 267-273.

%H N. J. A. Sloane, <a href="/classic.html#WYTH">Classic Sequences</a>

%F a(n) = B(A(n)), with A(k)=A000201(k) and B(k)=A001950(k) (Wythoff BA-numbers).

%F a(n) = A(n)+A(A(n)), with A(A(n))=A003622(n) (Wythoff AA-numbers).

%F Equals A022342(A003622(n)+1). - Michele Dondi (bik.mido(AT)tiscalenet.it), Dec 30 2001, sequence reference updated by _Peter Munn_, Nov 23 2017

%F a(n) = 2*A003622(n) - (n - 1) = A003623(n) - 1. - _Franklin T. Adams-Watters_, Jun 30 2009

%F A005713(a(n)) = 0. - _Reinhard Zumkeller_, Dec 30 2011

%F a(n) = A089910(n) - 2. - _Bob Selcoe_, Sep 21 2014

%p Digits := 100: t := (1+sqrt(5))/2; [ seq(2*floor((n+1)*t)+n,n=0..80) ];

%t Table[2*Floor[n*(1 + Sqrt[5])/2] + n - 1, {n, 50}] (* _Wesley Ivan Hurt_, Nov 21 2017 *)

%t Array[2 Floor[# GoldenRatio] + # - 1 &, 60] (* _Robert G. Wilson v_, Dec 12 2017 *)

%o (Haskell)

%o import Data.List (elemIndices)

%o a035336 n = a035336_list !! (n-1)

%o a035336_list = elemIndices 0 a005713_list

%o -- _Reinhard Zumkeller_, Dec 30 2011

%o (MAGMA) [2*Floor(n*(1+Sqrt(5))/2)+n-1: n in [1..80]]; // _Vincenzo Librandi_, Nov 19 2016

%o (Python)

%o from sympy import floor

%o from mpmath import phi

%o def a(n): return 2*floor(n*phi) + n - 1 # _Indranil Ghosh_, Jun 10 2017

%Y Cf. A022342, A066096.

%Y Cf. A139764, A089910, A194584.

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

%K nonn

%O 1,1

%A _N. J. A. Sloane_ and _J. H. Conway_

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 February 23 00:33 EST 2018. Contains 299473 sequences. (Running on oeis4.)