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 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.-P. Allouche, F. M. Dekking, Generalized Beatty sequences and complementary triples, arXiv:1809.03424 [math.NT], 2018. 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 STATUS approved

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Last modified December 10 04:15 EST 2019. Contains 329885 sequences. (Running on oeis4.)