A255773 Tree of lower Wythoff numbers (A000201) generated as the 1-component of the graph described at A095903.

1, 3, 4, 6, 8, 9, 12, 11, 14, 16, 21, 17, 22, 25, 33, 19, 24, 27, 35, 29, 37, 42, 55, 30, 38, 43, 56, 46, 59, 67, 88, 32, 40, 45, 58, 48, 61, 69, 90, 50, 63, 71, 92, 76, 97, 110, 144, 51, 64, 72, 93, 77, 98, 111, 145, 80, 101, 114, 148, 122, 156, 177, 232

Offset: 1

Author

Clark Kimberling, Mar 06 2015

Keywords

• nonn
• easy

Comments

This sequence and A255774 partition the positive integers.

Examples

			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.
		

Crossrefs

Cf. A000201, A095903, A244774.

Programs

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 *)