The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A055246 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A055246

At step number k >= 1 the 2^(k-1) open intervals that are erased from [0,1] in the Cantor middle-third set construction are I(k,n) = (a(n)/3^k, (1+a(n))/3^k), n=1..2^(k-1).
(history; published version)

#53 by N. J. A. Sloane at Sun Mar 13 19:13:00 EDT 2022

STATUS

editing

approved

#52 by N. J. A. Sloane at Sun Mar 13 19:12:57 EDT 2022

FORMULA

a(n) = 1+6*A005836(n), n >= 1. [Offset corrected by _Georg Fischer_, Mar 12 2022]

a(n) = 1+3*A005823(n), n >= 1. [Offset corrected by _Georg Fischer_, Mar 12 2022]

STATUS

proposed

editing

#51 by Georg Fischer at Sat Mar 12 06:30:35 EST 2022

STATUS

editing

proposed

Discussion

Sun Mar 13

09:27

Peter Luschny: I consider this a local minor correction that does not need to be signed if done by an editor. In such cases one should not generate noise with signatures that are longer than the signed item.

19:12

N. J. A. Sloane: I agree (as usual) with Peter

#50 by Georg Fischer at Sat Mar 12 06:30:27 EST 2022

FORMULA

a(n) = 1+6*A005836(n-1), n >= 1. [Offset corrected by _Georg Fischer_, Mar 12 2022]

a(n) = 1+3*A005823(n-1), n >= 1. [Offset corrected by _Georg Fischer_, Mar 12 2022]

STATUS

approved

editing

#49 by Peter Luschny at Sat Apr 24 03:30:16 EDT 2021

STATUS

reviewed

approved

#48 by Joerg Arndt at Sat Apr 24 02:16:19 EDT 2021

STATUS

proposed

reviewed

#47 by Michel Marcus at Fri Apr 23 05:28:58 EDT 2021

STATUS

editing

proposed

#46 by Michel Marcus at Fri Apr 23 05:28:41 EDT 2021

EXAMPLE

k=1: (1/3, 2/3);

k=2: (1/9, 2/9), (7/9, 8/9);

k=1: (1/3, 2/3); k=2: (1/9, 2/9), (7/9, 8/9); k=3: (1/27, 2/27), (7/27, 8/27), (19/27, 20/27), (25/27, 26/27); ...

STATUS

proposed

editing

#45 by Kevin Ryde at Fri Apr 23 04:45:05 EDT 2021

STATUS

editing

proposed

#44 by Kevin Ryde at Fri Apr 23 04:34:23 EDT 2021

COMMENTS

Let g(n) = Sum_{i=0..n} (i*binomial(n+i,i)^3*binomial(n,i)^2) = A112035(n). Let b = {m>0 : g(m) != 0 (mod 3)}. Then b(n) = a(n). - Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 08 2004

LINKS

R. Ralf Stephan, <a href="/somedcgf.html">Some divide-and-conquer sequences ...</a>

R. Ralf Stephan, <a href="/A079944/a079944.ps">Table of generating functions</a>

CROSSREFS

Cf. A003278, A005836, A005823, A055247, A112035.