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

1,2

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(2n) plus F(4n-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)

Links

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

Example

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,...).

Crossrefs

Cf. A000045, A035513, A173028, A220249.

Sequence in context: A346601 A242787 A031199 * A290014 A298225 A278919

Adjacent sequences: A173024 A173025 A173026 * A173028 A173029 A173030

Keyword

nonn

Author

Clark Kimberling, Feb 07 2010

Status

approved