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A151915 Wythoff AAAA numbers.

%I A151915 #28 Mar 19 2024 22:34:46
%S A151915 1,9,14,22,30,35,43,48,56,64,69,77,85,90,98,103,111,119,124,132,137,
%T A151915 145,153,158,166,174,179,187,192,200,208,213,221,229,234,242,247,255,
%U A151915 263,268,276,281,289,297,302,310,318,323,331,336,344,352,357,365,370,378
%N A151915 Wythoff AAAA numbers.
%C A151915 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.
%H A151915 A.H.M. Smeets, <a href="/A151915/b151915.txt">Table of n, a(n) for n = 1..20000</a>
%H A151915 Martin Griffiths, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Griffiths/gr48.html">On a Matrix Arising from a Family of Iterated Self-Compositions</a>, Journal of Integer Sequences, 18 (2015), #15.11.8.
%F A151915 a(n) = A(A(A(A(n)))) where A(n) = A000201(n);
%F A151915 a(n) = 3*floor(n*phi) + 2*n - 4 = 3*A000201(n) + 2*n - 4, where phi = (1+sqrt(5))/2.
%p A151915 A151915 := proc(n)
%p A151915     g := (1+sqrt(5))/2 ;
%p A151915     2*n-4+3*floor(n*g) ;
%p A151915 end proc:
%p A151915 seq(A151915(n),n=1..30) ; # _R. J. Mathar_, Jun 09 2018
%t A151915 a[n_] := 3 * Floor[n * GoldenRatio] + 2n - 4; Array[a, 100] (* _Amiram Eldar_, Dec 02 2018 *)
%o A151915 (PARI) a(n)=3*floor(n/2*(1+sqrt(5)))+2*n-4
%o A151915 (Python)
%o A151915 from math import isqrt
%o A151915 def A151915(n): return (n-2<<1)+((m:=n+isqrt(5*n**2))&-2)+(m>>1) # _Chai Wah Wu_, Aug 10 2022
%Y A151915 Cf. A001622, A000201 (Wythoff A numbers), A003622 (Wythoff AA numbers), A134859 (Wythoff AAA numbers).
%K A151915 nonn
%O A151915 1,2
%A A151915 _Benoit Cloitre_, Apr 12 2008