A173027 - OEIS

%I #12 Dec 13 2012 19:15:57

%S 1,3,4,5,16,19,22,25,28,31,34,97,105,113,121,129,137,145,153,161,169,

%T 177,185,193,201,209,217,225,233,631,652,673,694,715,736,757,778,799,

%U 820,841,862,883,904,925,946,967,988,1009,1030,1051,1072,1093,1114,1135

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

%C Row 1 of the array A173028.

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

%C 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 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

%C 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 K. G. Stier, <a href="/A173027/b173027.txt">Table of n, a(n) for n = 1..10000</a>

%e Referring to rows of the Wythoff array (A035513),

%e Row 1: (1,2,3,5,...) = 1*(1,2,3,...)

%e Row 3: (6,10,16,...) = 2*(3,5,8,...)

%e Row 4: (9,15,24,...) = 3*(3,5,8,...)

%e Row 5: (12,20,32,...) = 4*(3,5,8,...)

%e Row 16: (40,65,105...) = 8*(5,13,21,...).

%Y Cf. A000045, A035513, A173028, A220249.

%K nonn

%O 1,2

%A _Clark Kimberling_, Feb 07 2010