A216851 a(n) = T^(floor(log(n)/log(2)))(n) (see comment).

1, 1, 5, 1, 4, 5, 17, 1, 11, 4, 13, 5, 5, 17, 53, 1, 10, 11, 11, 4, 4, 13, 40, 5, 44, 5, 47, 17, 17, 53, 161, 1, 29, 10, 10, 11, 11, 11, 101, 4, 107, 4, 37, 13, 13, 40, 121, 5, 14, 44, 44, 5, 5, 47, 47, 17, 49, 17, 152, 53, 53, 161, 485, 1, 28, 29, 29, 10, 10, 10

Offset

1,3

Comments

T is the map T(x) = x/2 (x even) and T(x) = (3x+1)/2 (x odd) and T^(k)(x) = T^(k-1)(T(x)). This sequence has some arithmetical structures and fractal structures. For instance multiples of 3 are not in the sequence.

This is floor(log(n)/log(2)) iterations of the Collatz function applied to n. - T. D. Noe, Sep 25 2012

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Formula

Special values: a(2^k)=1, a(2^k-1)=2*3^(k-1)-1, a(4^k+1)=3^k+1, a(2*4^k+1)=3^(k+1)+2,...

Mathematica

T[n_] := If[EvenQ[n], n/2, (3 n + 1)/2]; Table[Nest[T, n, Floor[FullSimplify[Log[n]/Log[2]]]], {n, 100}] (* T. D. Noe, Sep 25 2012 *)

Prog

(PARI) T(x)=if(x%2, (3*x+1)/2, x/2);
p(m, n)=if(n<0, 0, t=0; s=n; while(t<m, s=T(s); t++); s);
a(n)=p(floor(log(n)/log(2)), n)

Crossrefs

Cf. A014682.

Sequence in context: A068468 A200022 A216157 * A179290 A342014 A355953

Adjacent sequences: A216848 A216849 A216850 * A216852 A216853 A216854

Keyword

nonn

Author

Benoit Cloitre, Sep 17 2012

Status

approved