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A047924 a(n) = B_{A_n+1}+1, where A_n = floor(n*phi) = A000201(n), B_n = floor(n*phi^2) = A001950(n) and phi is the golden ratio. 3
3, 6, 11, 14, 19, 24, 27, 32, 35, 40, 45, 48, 53, 58, 61, 66, 69, 74, 79, 82, 87, 90, 95, 100, 103, 108, 113, 116, 121, 124, 129, 134, 137, 142, 147, 150, 155, 158, 163, 168, 171, 176, 179, 184, 189, 192, 197, 202, 205, 210, 213, 218, 223, 226, 231, 234, 239 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

2nd column of array in A038150.

Apart from the first term also the second column of A126714; see also A223025. - Casey Mongoven, Mar 11 2013

REFERENCES

A. S. Fraenkel, Recent results and questions in combinatorial game complexities, Theoretical Computer Science, vol. 249, no. 2 (2000), 265-288.

Clark Kimberling, Stolarsky interspersions, Ars Combinatoria 39 (1995), 129-138.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

A. S. Fraenkel, Arrays, numeration systems and Frankenstein games, Theoret. Comput. Sci. 282 (2002), 271-284.

Clark Kimberling, The first column of an interspersion, The Fibonacci Quarterly 32 (1994), 301-315.

MAPLE

A001950 := proc(n)

        local phi;

        phi := (1+sqrt(5))/2 ;

        floor(n*phi^2) ;

end proc:

A000201 := proc(n)

        local phi;

        phi := (1+sqrt(5))/2 ;

        floor(n*phi) ;

end proc:

A047924 := proc(n)

        1+A001950(1+A000201(n)) ;

end proc: # R. J. Mathar, Mar 20 2013

MATHEMATICA

A[n_] := Floor[n*GoldenRatio]; B[n_] := Floor[n*GoldenRatio^2]; a[n_] := B[A[n]+1]+1; Table[a[n], {n, 0, 56}] (* Jean-Fran├žois Alcover, Feb 11 2014 *)

PROG

(Python)

from mpmath import *

mp.dps=100

import math

def A(n): return int(math.floor(n*phi))

def B(n): return int(math.floor(n*phi**2))

def a(n): return B(A(n) + 1) + 1 # Indranil Ghosh, Apr 25 2017

CROSSREFS

Cf. A007066.

Sequence in context: A246976 A189380 A047398 * A267519 A200182 A282277

Adjacent sequences:  A047921 A047922 A047923 * A047925 A047926 A047927

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Naohiro Nomoto, Jun 08 2001

New description from Aviezri S. Fraenkel, Aug 03 2007

STATUS

approved

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Last modified October 15 05:56 EDT 2018. Contains 316202 sequences. (Running on oeis4.)