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A151915 Wythoff AAAA numbers. 2
1, 9, 14, 22, 30, 35, 43, 48, 56, 64, 69, 77, 85, 90, 98, 103, 111, 119, 124, 132, 137, 145, 153, 158, 166, 174, 179, 187, 192, 200, 208, 213, 221, 229, 234, 242, 247, 255, 263, 268, 276, 281, 289, 297, 302, 310, 318, 323, 331, 336, 344, 352, 357, 365, 370, 378 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

In general Wythoff "AA...A" numbers, say A^(m)(n), with m A's, m>=1, are given by the formula: A^(m)(n) = F(m)*floor(n*Phi) + F(m-1)*n - F(m+1) + 1 where F are the Fibonacci numbers A000045.

LINKS

Table of n, a(n) for n=1..56.

Martin Griffiths, On a Matrix Arising from a Family of Iterated Self-Compositions, Journal of Integer Sequences, 18 (2015), #15.11.8.

FORMULA

a(n) = A(A(A(A(n)))) where A(n) = A000201(n);

a(n) = 3*floor(n*phi) + 2*n - 4 = 3*A000201(n) + 2*n - 4, where phi = (1+sqrt(5))/2.

MAPLE

A151915 := proc(n)

    g := (1+sqrt(5))/2 ;

    2*n-4+3*floor(n*g) ;

end proc:

seq(A151915(n), n=1..30) ; # R. J. Mathar, Jun 09 2018

MATHEMATICA

a[n_] := 3 * Floor[n * GoldenRatio] + 2n - 4; Array[a, 100] (* Amiram Eldar, Dec 02 2018 *)

PROG

(PARI) a(n)=3*floor(n/2*(1+sqrt(5)))+2*n-4

(Python)

from math import isqrt

def A151915(n): return (n-2<<1)+((m:=n+isqrt(5*n**2))&-2)+(m>>1) # Chai Wah Wu, Aug 10 2022

CROSSREFS

Cf. A001622, A000201 (Wythoff A numbers), A003622 (Wythoff AA numbers), A134859 (Wythoff AAA numbers).

Sequence in context: A272141 A289548 A001198 * A100263 A155082 A161547

Adjacent sequences:  A151912 A151913 A151914 * A151916 A151917 A151918

KEYWORD

nonn,changed

AUTHOR

Benoit Cloitre, Apr 12 2008

STATUS

approved

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Last modified August 11 15:10 EDT 2022. Contains 356066 sequences. (Running on oeis4.)