A174697 a(0)=a(1)=a(2)=1, a(n)=a(Floor[a(n-1)/2])+a(n-Floor[a(n-1)/2]).

1, 1, 1, 1, 2, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 8, 9, 9, 9, 10, 11, 12, 13, 13, 13, 14, 14, 15, 16, 17, 18, 18, 18, 18, 19, 19, 20, 21, 22, 22, 23, 24, 24, 24, 24, 24, 25, 25, 26, 27, 28, 28, 29, 29, 30, 30, 31, 31, 31, 31, 31, 32, 33, 33, 34, 35, 36, 36, 37, 37, 38, 38, 38, 39, 39, 40, 41, 41, 41, 41, 41, 42, 43, 44, 45, 45, 46, 47, 48, 48, 49, 49, 50, 50, 50, 51, 51, 51, 52, 53

Offset

0,5

Comments

Based on Conway's internal recursive structure, this sequence need a minimum start sequence of three ones ( here four are used) followed by a two to get started and has two alternating modes for the limiting ratio a(n+1)/a(n).

Links

Table of n, a(n) for n=0..100.

Mathematica

a[0] = 1; a[1] = 1; a[2] = 1; a[3] = 1; a[4] = 2;
a[n_] := a[n] = a[Floor[a[n - 1]/2]] + a[n - Floor[a[n - 1]/2]]
Table[a[n], {n, 0, 100}]

Crossrefs

Cf. A004001.

Sequence in context: A360924 A027434 A319434 * A176504 A196162 A071940

Adjacent sequences: A174694 A174695 A174696 * A174698 A174699 A174700

Keyword

nonn

Author

Roger L. Bagula, Nov 30 2010

Status

approved