The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A285681 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A285681

Positions of 0 in A285680.
(history; published version)

#8 by Hugo Pfoertner at Sat Jul 27 03:54:07 EDT 2024

STATUS

reviewed

approved

#7 by Joerg Arndt at Sat Jul 27 03:15:38 EDT 2024

STATUS

proposed

reviewed

#6 by Jason Yuen at Sat Jul 27 03:15:02 EDT 2024

STATUS

editing

proposed

#5 by Jason Yuen at Sat Jul 27 03:14:56 EDT 2024

CROSSREFS

Cf. A003849, A285680, A258682, A285682, A285683.

STATUS

approved

editing

#4 by N. J. A. Sloane at Fri May 12 00:15:18 EDT 2017

STATUS

proposed

approved

#3 by Clark Kimberling at Thu May 11 21:33:20 EDT 2017

STATUS

editing

proposed

#2 by Clark Kimberling at Thu May 11 21:07:34 EDT 2017

NAME

allocated for Clark KimberlingPositions of 0 in A285680.

DATA

1, 3, 4, 6, 8, 9, 11, 13, 15, 16, 18, 20, 21, 23, 25, 27, 28, 30, 32, 34, 35, 37, 39, 40, 42, 44, 46, 47, 49, 51, 52, 54, 56, 58, 59, 61, 63, 65, 66, 68, 70, 71, 73, 75, 77, 78, 80, 82, 84, 85, 87, 89, 90, 92, 94, 96, 97, 99, 101, 102, 104, 106, 108, 109

OFFSET

1,2

COMMENTS

A 3-way partition of the positive integers, by positions of 0, 1, 2 in A285680:

A285681: positions of 0; slope t = (15+sqrt(5))/10;

A285682: positions of 1; slope u = (4+sqrt(5);

A285683: positions of 2; slope v = (1+3*sqrt(5))/2;

where 1/t + 1/u + 1/v = 1. Conjecture: a(n) - a(n-1) is in {1,2} for n>=2.

LINKS

Clark Kimberling, <a href="/A285681/b285681.txt">Table of n, a(n) for n = 1..10000</a>

MATHEMATICA

s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {0}}] &, {0}, 13] ; (* A003849 *)

w = StringJoin[Map[ToString, s]]

w1 = StringReplace[w, {"1010" -> "2"}]

st = ToCharacterCode[w1] - 48; (* A285680 *)

Flatten[Position[st, 0]]; (* A285681 *)

Flatten[Position[st, 1]]; (* A285682 *)

Flatten[Position[st, 2]]; (* A285683 *)

CROSSREFS

Cf. A003849, A285680, A258682, A285683.

KEYWORD

allocated

nonn,easy

AUTHOR

Clark Kimberling, May 11 2017

STATUS

approved

editing

#1 by Clark Kimberling at Mon Apr 24 17:46:19 EDT 2017

NAME

allocated for Clark Kimberling

KEYWORD

allocated

STATUS

approved