A099810 a(n) = a(n-1) XOR (a(n-1) + a(n-2)), with a(1)=1, a(2)=3, where XOR is the binary exclusive OR operation.

1, 3, 7, 13, 25, 63, 103, 193, 489, 835, 1647, 4061, 6545, 12543, 31343, 53505, 105073, 258307, 424567, 790797, 2005641, 3420447, 6748855, 16634209, 26811769, 51377059, 128377535, 219165917, 430383937, 1058044767, 1739056639

Offset

1,2

Links

Table of n, a(n) for n=1..31.

Example

a(3) = 7 since 3 XOR (3+1) = 3 XOR 4 = 7.
a(4) = 13 since 7 XOR (7+3) = 7 XOR 10 = 13.
a(5) = 25 since 13 XOR (13+7) = 13 XOR 20 = 25.
The binary expansions of a(n) form a triangle (listed with ones place in leftmost column):
1,
1,1,
1,1,1,
1,0,1,1,
1,0,0,1,1,
1,1,1,1,1,1,
1,1,1,0,0,1,1,
1,0,0,0,0,0,1,1,
1,0,0,1,0,1,1,1,1,
1,1,0,0,0,0,1,0,1,1,
1,1,1,1,0,1,1,0,0,1,1,
1,0,1,1,1,0,1,1,1,1,1,1,...

Prog

(PARI) a(n)=if(n==1, 1, if(n==2, 3, bitxor(a(n-1), a(n-1)+a(n-2))))

Crossrefs

Cf. A099811.

Sequence in context: A363143 A282913 A284026 * A283177 A284297 A205521

Adjacent sequences: A099807 A099808 A099809 * A099811 A099812 A099813

Keyword

nonn

Author

Paul D. Hanna, Oct 26 2004

Status

approved