The On-Line Encyclopedia of Integer Sequences (OEIS)

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A305496

Positions of 2 in the fixed point of the morphism 0->120, 1->110, 2->100 applied to 1 (as in A305490).
(history; published version)

#10 by Michel Marcus at Tue Jul 16 02:34:57 EDT 2024

STATUS

reviewed

approved

#9 by Kevin Ryde at Tue Jul 16 01:45:45 EDT 2024

STATUS

proposed

reviewed

#8 by Jason Yuen at Mon Jul 15 21:28:29 EDT 2024

STATUS

editing

proposed

#7 by Jason Yuen at Mon Jul 15 21:28:26 EDT 2024

EXAMPLE

Positions of 2: (8,17,26,35,44,53,62,68, ... ) = A305469A305496

STATUS

approved

editing

#6 by Harvey P. Dale at Tue May 03 19:07:33 EDT 2022

STATUS

editing

approved

#5 by Harvey P. Dale at Tue May 03 19:07:27 EDT 2022

MATHEMATICA

Position[SubstitutionSystem[{0->{1, 2, 0}, 1->{1, 1, 0}, 2->{1, 0, 0}}, {1}, {6}][[1]], 2]//Flatten (* Harvey P. Dale, May 03 2022 *)

STATUS

approved

editing

#4 by Susanna Cuyler at Sat Jun 02 21:30:43 EDT 2018

STATUS

proposed

approved

#3 by Clark Kimberling at Sat Jun 02 15:18:05 EDT 2018

STATUS

editing

proposed

#2 by Clark Kimberling at Sat Jun 02 15:17:17 EDT 2018

NAME

allocated for Clark KimberlingPositions of 2 in the fixed point of the morphism 0->120, 1->110, 2->100 applied to 1 (as in A305490).

DATA

8, 17, 26, 35, 44, 53, 62, 68, 71, 80, 89, 98, 107, 116, 125, 134, 143, 149, 152, 161, 170, 179, 188, 197, 206, 215, 224, 230, 233, 242, 251, 260, 269, 278, 287, 296, 305, 311, 314, 323, 332, 341, 350, 359, 368, 377, 386, 392, 395, 404, 413, 422, 431, 440

OFFSET

1,1

COMMENTS

Let u, v, w be the position sequences of 0,1,2 in A305490. They partition the positive integers, and v is also the position sequence of 0 in Stewart's choral sequence, A116178.

LINKS

Clark Kimberling, <a href="/A305496/b305496.txt">Table of n, a(n) for n = 1..10000</a>

EXAMPLE

Fixed point: (1, 1, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 1, 0, 1, 2, 0, 1, 1, ... )

Positions of 0: (3,6,9,12,15,18,21,23, ... ) = A305495

Positions of 1: (1,2,4,5,7,10,11,13,14, ... ) = A189636

Positions of 2: (8,17,26,35,44,53,62,68, ... ) = A305469

MATHEMATICA

z = 120;

t = Nest[Flatten[# /. {0 -> {1, 2, 0}, 1 -> {1, 1, 0},

2 -> {1, 0, 0}}] &, {0}, 9]; (* A305490 *)

Take[Flatten[Position[t, 0]], z] (* A305495 *)

Take[Flatten[Position[t, 1]], z] (* A116178 *)

Take[Flatten[Position[t, 2]], z] (* A305496 *)

CROSSREFS

Cf. A305490, A116178, A305495.

KEYWORD

allocated

nonn,easy

AUTHOR

Clark Kimberling, Jun 02 2018

STATUS

approved

editing

#1 by Clark Kimberling at Sat Jun 02 14:03:45 EDT 2018

NAME

allocated for Clark Kimberling

KEYWORD

allocated

STATUS

approved