The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A138967 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A138967

Infinite Fibonacci word on the alphabet {1,2,3,4}.
(history; published version)

#21 by Bruno Berselli at Thu Sep 28 09:00:43 EDT 2017

STATUS

reviewed

approved

#20 by Joerg Arndt at Thu Sep 28 08:53:01 EDT 2017

STATUS

proposed

reviewed

#19 by Bruno Berselli at Thu Sep 28 08:40:45 EDT 2017

STATUS

editing

proposed

#18 by Bruno Berselli at Thu Sep 28 08:40:41 EDT 2017

FORMULA

a(n) = 3 for n = 3, 8, 21, 55, ..., F(2k2*k), where k>1.

a(n) = 4 for n = 5, 13, 34, 89, ..., F(2k2*k+1), where k>1.

STATUS

proposed

editing

#17 by Michel Dekking at Thu Sep 28 08:29:38 EDT 2017

STATUS

editing

proposed

#16 by Michel Dekking at Thu Sep 28 08:28:49 EDT 2017

COMMENTS

(a(n)) is the unique fixed point of the morphism 1->12, 2->3, 3->14, 4->3, obtained by coding the overlapping 3-block morphism of the Fibonacci morphism according to 010<->1, 100<->2, 001<->3, 101<->4. - Michel Dekking, Sep 28 2017

CROSSREFS

Cf. A000201, A001950, A003849, A101864, A270788, A276757.

STATUS

approved

editing

#15 by Peter Luschny at Fri Aug 19 02:20:10 EDT 2016

STATUS

reviewed

approved

#14 by Joerg Arndt at Thu Aug 18 02:19:51 EDT 2016

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proposed

reviewed

#13 by Michel Marcus at Thu Aug 18 02:17:11 EDT 2016

STATUS

editing

proposed

#12 by Michel Marcus at Thu Aug 18 02:16:49 EDT 2016

COMMENTS

Start with the infinite Fibonacci word A003849, which is 0100101001001010010... and replace each 0 by 1,2,3 and each 1 by 1,4.

0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 ... and replace

each 0 by 1,2,3 and each 1 by 1,4; the result is A138967.

Discussion

Thu Aug 18

02:17

Michel Marcus: Edited comment