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A035337 Third column of Wythoff array. 13
3, 11, 16, 24, 32, 37, 45, 50, 58, 66, 71, 79, 87, 92, 100, 105, 113, 121, 126, 134, 139, 147, 155, 160, 168, 176, 181, 189, 194, 202, 210, 215, 223, 231, 236, 244, 249, 257, 265, 270, 278, 283, 291, 299, 304, 312 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Also, positions of 3's in A139764, the smallest term in Zeckendorf representation of n. - John W. Layman, Aug 25 2011

The formula a(n) = 3*A003622(n)-n+1 = 3AA(n)-n+1 conjectured by Layman below is correct, since it is well known that AA(n)+1 = B(n) = A(n)+n, where B = A001950, and so 3AA(n)-n+1 = 3B(n)-n-2 = 3A(n)+2n-2. - Michel Dekking, Aug 31 2017

LINKS

Table of n, a(n) for n=0..45.

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

N. J. A. Sloane, Classic Sequences

FORMULA

a(n) = F(4)A(n)+F(3)(n-1) = 3A(n)+2n-2, where A = A000201 and F = A000045. - Michel Dekking, Aug 31 2017

It appears that a(n) = 3*A003622(n) - n + 1. - John W. Layman, Aug 25 2011

MAPLE

t := (1+sqrt(5))/2 ; [ seq(3*floor((n+1)*t)+2*n, n=0..80) ];

MATHEMATICA

Table[3 Floor[n GoldenRatio] + 2 n - 2, {n, 46}] (* Michael De Vlieger, Aug 31 2017 *)

PROG

(Python)

from sympy import floor

from mpmath import phi

def a(n): return 3*floor((n + 1)*phi) + 2*n # Indranil Ghosh, Jun 10 2017

(PARI) a(n) = 2*n + 3*floor((1+sqrt(5))*(n+1)/2); \\ Altug Alkan, Sep 18 2017

CROSSREFS

Cf. A139764.

Let A = A000201, B = A001950. Then AA = A003622, AB = A003623, BA = A035336, BB = A101864. The eight triples AAA, AAB, ..., BBB are A134859, A134860, A035337, A134862, A134861, A134863, A035338, A134864, resp.

Sequence in context: A158507 A030765 A198515 * A029500 A243770 A216911

Adjacent sequences:  A035334 A035335 A035336 * A035338 A035339 A035340

KEYWORD

nonn,changed

AUTHOR

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

STATUS

approved

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Last modified December 13 00:17 EST 2017. Contains 295954 sequences.