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A035336 a(n) = 2*floor(n*phi) + n - 1, where phi = (1+sqrt(5))/2. 31
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).

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) ];

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

Equals A022342(A066096(n)).

Cf. A003622, A022342, A066094, 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

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Last modified December 12 16:38 EST 2017. Contains 295949 sequences.