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

2, 9, 13, 45, 56, 67, 78, 89, 262, 291, 320, 349, 378, 407, 436, 465, 494, 523, 552, 581, 610, 1673, 1749, 1825, 1901, 1977, 2053, 2129, 2205, 2281, 2357, 2433, 2509, 2585, 2661, 2737, 2813, 2889, 2965, 3041, 3117, 3193, 3269, 3345, 3421, 3497, 3573, 3649

Offset

1,1

Comments

This sequence is corresponding to A173027. Also Row 2 of the array A173028.

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;

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

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.

Links

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

Example

Referring to rows of the Wythoff array (A035513),
Row 2: (4,7,11,18,...) = 1*(4,7,11,18,29,47,76,...)
Row 9: (22,36,58,...) = 2*(11,18,29,47,76...)
Row 13: (33,54,87,...) = 3*(11,18,29,47,76...)
Row 45: (116,188,304,...) = 4*(29,47,76...)

Crossrefs

Cf. A173027, A035513, A173028, A002878, A001519.

Sequence in context: A178688 A163735 A144472 * A071343 A043401 A226953

Adjacent sequences: A220246 A220247 A220248 * A220250 A220251 A220252

Keyword

nonn

Author

K. G. Stier, Dec 08 2012

Status

approved