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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
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 (list; graph; refs; listen; history; text; internal format)
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: A082233 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

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Last modified June 17 07:00 EDT 2019. Contains 324183 sequences. (Running on oeis4.)