cp's OEIS Frontend

A220249 Numbers of rows R of the Wythoff array such that R is the n-th multiple of a tail of the Lucas sequence.

%I A220249 #15 Dec 13 2012 19:15:42
%S A220249 2,9,13,45,56,67,78,89,262,291,320,349,378,407,436,465,494,523,552,
%T A220249 581,610,1673,1749,1825,1901,1977,2053,2129,2205,2281,2357,2433,2509,
%U A220249 2585,2661,2737,2813,2889,2965,3041,3117,3193,3269,3345,3421,3497,3573,3649
%N A220249 Numbers of rows R of the Wythoff array such that R is the n-th multiple of a tail of the Lucas sequence.
%C A220249 This sequence is corresponding to A173027. Also Row 2 of the array A173028.
%C A220249 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 odd-indexed Lucas numbers (A002878) while m is equal to odd-indexed Fibonacci numbers (A001519). Example: from n=988 to 2584 d=3571 and m=1597;
%C A220249 Also of interest are the gaps between two consecutive groups which appear to be sums of one Lucas number L(2n+1) plus one Fibonacci number F(4n). Example: gap 5 after a(55) is 6964 = L(11) + F(20) = 199 + 6765
%C A220249 Likewise, the tail (as mentioned in this sequence's name) of the Lucas sequence is chopped off by two initial terms at each of the gap positions.
%H A220249 K. G. Stier, <a href="/A220249/b220249.txt">Table of n, a(n) for n = 1..10000</a>
%e A220249 Referring to rows of the Wythoff array (A035513),
%e A220249 Row 2: (4,7,11,18,...) = 1*(4,7,11,18,29,47,76,...)
%e A220249 Row 9: (22,36,58,...) = 2*(11,18,29,47,76...)
%e A220249 Row 13: (33,54,87,...) = 3*(11,18,29,47,76...)
%e A220249 Row 45: (116,188,304,...) = 4*(29,47,76...)
%Y A220249 Cf. A173027, A035513, A173028, A002878, A001519.
%K A220249 nonn
%O A220249 1,1
%A A220249 _K. G. Stier_, Dec 08 2012