A096016 A modified Fibonacci sequence controlled by a toggle switch. The toggle switch (initial state of 2) flips between 2 and 3 after each reduction.

0, 1, 1, 2, 3, 5, 4, 3, 7, 5, 4, 9, 13, 11, 8, 19, 27, 23, 50, 73, 41, 57, 98, 155, 253, 136, 389, 525, 457, 982, 1439, 807, 1123, 1930, 3053, 1661, 2357, 4018, 2125, 6143, 4134, 10277, 14411, 24688, 13033, 37721, 25377, 63098, 88475, 151573, 80016, 231589

Offset

0,4

Comments

Initial state: a(1)=0, a(2)=1, j=2; thereafter a(n) = a(n-1) + a(n-2) and if a(n)>2, j=2 and a(n) == 0 (mod 2) then a(n) = a(n)/j and j=3; if a(n)>3, j=3 and a(n) == 0 (mod 3) then a(n) = a(n)/j and j=2.

Links

Table of n, a(n) for n=0..51.

Example

a(0) = 0 by definition and the initial state of the toggle switch is 2;
a(1) = 1 by definition;
a(2) = 0+1 = 1;
a(3) = 1+1 = 2;
a(4) = 1+2 = 3;
a(5) = 2+3 = 5;
a(6) = 3+5 => 8 => 4 since 8 > 2, therefore 8/2 = 4 and toggle the switch from 2 to 3;
a(7) = 5+4 => 9 => 3 since 9 is > 3, therefore 9/3 = 3 and toggle the switch from 3 back to 2;
a(8) = 4+3 = 7;
a(9) = 3+7 => 10 => 5 since 10 is > 2, therefore 10/2 = 5 and toggle the switch to 3;
a(10) = 7+5 => 12 => 4 since 12 is > 3, therefore 12/3 = 4 and toggle the switch to 2;
a(11) = 5+4 = 9, cannot reduce by the toggle switch because 9/2 is not an integer;
a(12) = 4+9 = 13;
a(13) = 9+13 => 22 => 11 and toggle the switch to 3;
a(14) = 13+11 => 24 => 8 and set the toggle switch to 2;
a(15) = 11+8 = 19, etc.

Mathematica

a[0] = 0; a[1] = 1; ts = 0; a[n_] := a[n] = Block[{b = a[n - 1] + a[n - 2]}, If[ IntegerQ[ b / (ts + 2)] && b > 3, b = b/(ts + 2); ts = Mod[ts + 1, 2]]; b]; Table[ a[n], {n, 0, 52}] (* Robert G. Wilson v, Jul 21 2004 *)

Crossrefs

Sequence in context: A330806 A058981 A117339 * A123274 A214674 A185332

Adjacent sequences: A096013 A096014 A096015 * A096017 A096018 A096019

Keyword

nonn

Author

Pierre CAMI, Jul 20 2004

Extensions

Edited by Robert G. Wilson v, Jul 21 2004

Status

approved