cp's OEIS Frontend

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

%I A173027 #16 Aug 15 2025 00:58:17
%S A173027 1,3,4,5,16,19,22,25,28,31,34,97,105,113,121,129,137,145,153,161,169,
%T A173027 177,185,193,201,209,217,225,233,631,652,673,694,715,736,757,778,799,
%U A173027 820,841,862,883,904,925,946,967,988,1009,1030,1051,1072,1093,1114,1135
%N A173027 Numbers of rows R of the Wythoff array such that R is the n-th multiple of a tail of the Fibonacci sequence.
%C A173027 Row 1 of the array A173028.
%C A173027 Contribution from _K. G. Stier_, Dec 08 2012: (Start)
%C A173027 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;
%C A173027 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.
%C A173027 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)
%H A173027 K. G. Stier, <a href="/A173027/b173027.txt">Table of n, a(n) for n = 1..10000</a>
%e A173027 Referring to rows of the Wythoff array (A035513),
%e A173027 Row 1: (1,2,3,5,...) = 1*(1,2,3,...)
%e A173027 Row 3: (6,10,16,...) = 2*(3,5,8,...)
%e A173027 Row 4: (9,15,24,...) = 3*(3,5,8,...)
%e A173027 Row 5: (12,20,32,...) = 4*(3,5,8,...)
%e A173027 Row 16: (40,65,105...) = 8*(5,13,21,...).
%Y A173027 Cf. A000045, A035513, A173028, A220249.
%K A173027 nonn
%O A173027 1,2
%A A173027 _Clark Kimberling_, Feb 07 2010