A183090 Tree generated by A005652, associated with numbers which are not the sum of two Fibonacci numbers.

1, 2, 3, 4, 6, 5, 8, 7, 11, 12, 9, 10, 16, 15, 14, 13, 21, 23, 22, 25, 17, 18, 19, 20, 30, 33, 29, 31, 27, 28, 24, 26, 42, 41, 45, 46, 43, 44, 50, 49, 32, 34, 35, 36, 37, 38, 40, 39, 58, 60, 64, 67, 56, 59, 61, 62, 53, 54, 55, 57, 48, 47, 51, 52

Offset

1,2

Comments

A permutation of the positive integers. See the comment at A183079.

Links

Table of n, a(n) for n=1..64.

Formula

Let L(n)=A005652(n) and U(n)=A005653(n), these being complementary sequences, each comprising a maximal set no two of whose elements is a Fibonacci number.

The tree-array T(n,k) is then given by rows:

T(0,0)=1; T(1,0)=2;

T(n,2*j)=L(T(n-1,j));

T(n,2*j+1)=U(T(n-1,j));

for j=0,1,...,2^(n-1)-1, n>=2.

Example

Top 5 rows:
  1;
  2;
  3,             4;
  6,      5,     8,      7;
  11, 12, 9, 10, 16, 15, 14, 13;
From row 3 to row 4: 3->(6,5) and 4->(8,7). For all such pairs, the 1st component is in L and the 2nd, in U.

Crossrefs

Cf. A005652, A005653, A183079, A074049.

Sequence in context: A299759 A372030 A232560 * A232559 A094138 A116538

Adjacent sequences: A183087 A183088 A183089 * A183091 A183092 A183093

Keyword

nonn,tabf

Author

Clark Kimberling, Dec 24 2010

Status

approved