1,2

(1) Every positive integer occurs exactly once, so that this is a

permutation of the natural numbers.

(2) Obtained from the preliminary Wyhoff triangle (A1663109) by arranging

each row in increasing order.

(3) The difference between consecutive row terms is a Fibonacci

number (A000045).

(4) Is the difference between consecutive column terms a Fibonacci number?

Clark Kimberling, "The Wythoff triangle and unique representations of positive integers," preprint, 2009.

For a=1,2,3,... and b=0,1,...,a-1, let P(a,b) be the number of the

row of the Wythoff array (A035513) that precurses to (a,b). Then

for each a, arrange the numbers P(a,b) in increasing order.

The first nine rows of T:

1

2....3

4....6...8

5....7...9..11

10..12..14..16..21

13..15..17..19..24..29

18..20..22..27..32..37..42

23..25..30..35..40..45..50..55

26..28..33..38..43..48..53..58..63

Row 5 of the preliminary Wythoff triangle is

16,21,10,12,14, so that row 5 of the Wythoff triangle is

10,12,14,16,21. These are the row numbers of the Wythoff

array W (A035513) which precurse to pairs (5,b) for b=0,1,2,3,4,

not respectively. Example of precursion: row 16 of W is

40,65,105,...; then 65-40=25, 40-25=15, 25-15=10, 15-10=5,

10-5=5, 5-5=0, 5-0=5, so that the initial pair (5,0) was reached

in seven precursive steps.

Cf. A035513, A165357, A166309.

Sequence in context: A069912 A152306 A120817 this_sequence A109852 A083197 A038150

Adjacent sequences: A166307 A166308 A166309 this_sequence A166311 A166312 A166313

nonn,tabl

Clark Kimberling (ck6(AT)evansville.edu), Oct 11 2009