A183090 - OEIS

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

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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; F(1,0)=2;

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

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

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

EXAMPLE

Top 5 rows:

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.