

A140357


a(1)=1; a(n)=floor(4*a(n1)*(na(n1)) / n) for n > 1.


1



1, 2, 2, 4, 3, 6, 3, 7, 6, 9, 6, 12, 3, 9, 14, 7, 16, 7, 17, 10, 20, 7, 19, 15, 24, 7, 20, 22, 21, 25, 19, 30, 10, 28, 22, 34, 11, 31, 25, 37, 14, 37, 20, 43, 7, 23, 46, 7, 24, 49, 7, 24, 52, 7, 24, 54, 11, 35, 56, 14, 43, 52, 36, 63, 7, 25, 62, 21, 58, 39, 70, 7, 25, 66, 31, 73, 15, 48
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OFFSET

1,2


COMMENTS

a(n)/n approximates the behavior of the logistic map x(n+1) = r*x(n)*(1x(n)) at the critical value r = 4 where its iterated behavior becomes chaotic.
Conjecture: starting with any given n and any 1 <= a(n) <= n and applying the rule for the sequence produces a sequence which eventually joins this one. For example, starting with a(9)=5, the sequence continues 10,3,9,11,9, at which point it has joined.
There is a number x(1) such that iterating the logistic map x(n+1) = 4*x(n)*(1x(n)) approaches a(n)/n; in particular x(n) > 1/2 iff a(n)/n > 1/2 and lim_{n>infinity} x(n)a(n)/n = 0. x(1) is approximately 0.74300456748016924159182578873962328734252790178266693834898117732270042549583799064232908893034253248. It appears that x(n)a(n)/n < 1/sqrt(n) for all n.


LINKS



MATHEMATICA

a[1]=1; a[n_]:=a[n]=Floor[(4a[n1](na[n1]))/n]; Table[a[n], {n, 100}] (* Harvey P. Dale, Mar 28 2011 *)
nxt[{n_, a_}]:={n+1, Floor[4a (n+1a)/(n+1)]}; NestList[nxt, {1, 1}, 80][[All, 2]] (* Harvey P. Dale, Dec 22 2019 *)


CROSSREFS



KEYWORD

easy,nonn


AUTHOR



STATUS

approved



