A173027 Numbers of rows R of the Wythoff array such that R is the n-th multiple of a tail of the Fibonacci sequence.

1, 3, 4, 5, 16, 19, 22, 25, 28, 31, 34, 97, 105, 113, 121, 129, 137, 145, 153, 161, 169, 177, 185, 193, 201, 209, 217, 225, 233, 631, 652, 673, 694, 715, 736, 757, 778, 799, 820, 841, 862, 883, 904, 925, 946, 967, 988, 1009, 1030, 1051, 1072, 1093, 1114, 1135

Offset: 1

Author

Clark Kimberling, Feb 07 2010

Keywords

• nonn

Comments

Row 1 of the array A173028.

Contribution from K. G. Stier, Dec 08 2012: (Start)

It appears that the numbers of this sequence form groups of m members respectively with same distance d of two consecutive values a(n) such that d is equal to even-indexed Fibonacci numbers (A001906) while m is equal to even-indexed Lucas numbers (A005248). Example: from n=1365 to 3571 d=987 and m=2207;

Also of interest are the gaps between two consecutive groups which appear to be sums of Fibonacci numbers F(2*n) plus F(4*n-2). Example: gap 5 after a(76) is 2639 = F(10) + F(18) = 55 + 2584.

Likewise, the tail (as mentioned in this sequence's name) of the Fibonacci sequence is chopped off by two initial terms at each of the gap positions. (End)

Examples

			Referring to rows of the Wythoff array (A035513),
Row 1: (1,2,3,5,...) = 1*(1,2,3,...)
Row 3: (6,10,16,...) = 2*(3,5,8,...)
Row 4: (9,15,24,...) = 3*(3,5,8,...)
Row 5: (12,20,32,...) = 4*(3,5,8,...)
Row 16: (40,65,105...) = 8*(5,13,21,...).
		

Links

• K. G. Stier, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000045, A035513, A173028, A220249.