A255774 Tree of upper Wythoff numbers (A001950) generated as the 2-component of the graph described at A095903.

2, 5, 7, 10, 13, 15, 20, 18, 23, 26, 34, 28, 36, 41, 54, 31, 39, 44, 57, 47, 60, 68, 89, 49, 62, 70, 91, 75, 96, 109, 143, 52, 65, 73, 94, 78, 99, 112, 146, 81, 102, 115, 149, 123, 157, 178, 233, 83, 104, 117, 151, 125, 159, 180, 235, 130, 164, 185, 240, 198

Offset

1,1

Comments

This sequence and A255773 partition the positive integers.

Links

Table of n, a(n) for n=1..60.

Example

To generate the tree of lazy Fibonacci representations as in A095903, start with 1,2. Suffix the next two Fibonacci numbers, getting 1+2, 1+3; 2+3, 2+5. Suffix the next two Fibonacci numbers, getting 1+2+3, 1+2+5, 1+3+5, 1+3+8; 2+3+5, 2+3+8, 2+5+8, 2+5+13. Continue forever. A255773 is the tree of numbers having root (initial summand) 1, and A255774 is the tree of numbers having root (initial summand) 2.

Mathematica

width = 6; t = Map[Total, Fibonacci[Flatten[NestList[Flatten[Map[{Join[#, {Last[#] +1}], Join[#, {Last[#] + 2}]} &, #], 1] &, {{2}, {3}}, width], 1]]](*A095903*)
Map[t[[#]] &, Apply[Range, {2^Range[#] - 1, 3 2^(Range[#] - 1) - 2}]] &[width + 1] (*A255773*)
Map[t[[#]] &, Apply[Range, {3 2^(Range[#] - 1) - 1, 2 (2^Range[#] - 1)}]] &[width + 1] (*A255774*) (* Peter J. C. Moses, Mar 06 2015 *)

Crossrefs

Cf. A001950, A095903, A244773.

Sequence in context: A285207 A140398 A344988 * A364005 A081838 A057347

Adjacent sequences: A255771 A255772 A255773 * A255775 A255776 A255777

Keyword

nonn,easy

Author

Clark Kimberling, Mar 06 2015

Status

approved