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A080426 a(1)=1, a(2)=3; all terms are either 1 or 3; each run of 3's is followed by a run of two 1's; and a(n) is the length of the n-th run of 3's. 6
1, 3, 1, 1, 3, 3, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 3, 3, 1, 1, 3, 3, 3, 1, 1, 3, 3, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 3, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 3, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 3, 3, 1, 1, 3, 3, 3, 1, 1, 3, 3, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 3, 3, 1, 1, 3, 3, 3, 1, 1, 3, 3, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 3, 3, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

It appears that the sequence can be calculated by any of the following three methods: (1) Start with 1 and repeatedly replace (simultaneously) all 1's with 1,3,1 and all 3's with 1,3,3,3,1. (2) a(n)= A026490(2n). (3) Replace each 2 in A026465 (run lengths in Thue-Morse) with 3.

Length of n-th run of 1's in the Feigenbaum sequence A035263 = 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, .... - Philippe Deléham, Apr 18 2004

Another construction. Let S_0 = 1, and let S_n be obtained by applying the morphism 1 -> 3, 3 -> 113 to S_{n-1}. The sequence is the concatenation S_0, S_1, S_2, ... - D. R. Hofstadter, Oct 23 2014

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

D. R. Hofstadter, Anti-Fibonacci numbers, Oct 23 2014

FORMULA

a(1) = 1; for n>1, a(n) = A003156(n) - A003156(n-1). - Philippe Deléham, Apr 16 2004

MATHEMATICA

Position[ Nest[ Flatten[# /. {0 -> {0, 2, 1}, 1 -> {0}, 2 -> {0}}]&, {0}, 8], 0] // Flatten // Differences // Prepend[#, 1]& (* Jean-François Alcover, Mar 14 2014, after Philippe Deléham *)

PROG

(Haskell)  following Deléham

import Data.List (group)

a080426 n = a080426_list !! n

a080426_list = map length $ filter ((== 1) . head) $ group a035263_list

-- Reinhard Zumkeller, Oct 27 2014

CROSSREFS

Cf. A026465, A026490, A035263, A003156.

Arises in the analysis of A075326, A249031 and A249032.

Sequence in context: A094782 A035666 A060592 * A230293 A133116 A059959

Adjacent sequences:  A080423 A080424 A080425 * A080427 A080428 A080429

KEYWORD

nonn

AUTHOR

John W. Layman, Feb 18 2003

STATUS

approved

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Last modified September 20 12:42 EDT 2018. Contains 315239 sequences. (Running on oeis4.)