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

1,2

Comments

This sequence and A255774 partition the positive integers.

Links

Table of n, a(n) for n=1..63.

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. A000201, A095903, A244774.

Sequence in context: A188015 A192284 A024324 * A195019 A288601 A192519

Adjacent sequences: A255770 A255771 A255772 * A255774 A255775 A255776

Keyword

nonn,easy

Author

Clark Kimberling, Mar 06 2015

Status

approved