The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A072998 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A072998

To get a(n), write n in balanced ternary notation (using only digits -1, 0, 1, -1), then change -1's to 0's, 0's to 1's, and 1's to 2's.
(history; published version)

#22 by N. J. A. Sloane at Wed Mar 31 04:54:48 EDT 2021

STATUS

editing

approved

#21 by N. J. A. Sloane at Wed Mar 31 04:54:45 EDT 2021

EXAMPLE

n balanced ternary a(n)

-----------------------

0........0...........1

1........1...........2

2......1,-1..........2,0

3.......1,0..........2,1

...

STATUS

approved

editing

#20 by N. J. A. Sloane at Wed Mar 31 04:51:05 EDT 2021

STATUS

editing

approved

#19 by N. J. A. Sloane at Wed Mar 31 04:51:01 EDT 2021

NAME

Numbers To get a(n), write n in balanced ternary notation (using only digits -1, 0, 1, -1), then change -1's to 0's, 0's to 1's, and 1's to 2's.

LINKS

Ken Levasseur, <a href="http://discretemath.org/ternary_number_system.html">The Balanced Ternary Number System</a>

EXAMPLE

11d 11 in base 10 = 11_10 = {1,1,-1} in balanced ternary = 1*3^2 + 1*3^1 - 1*3^0. Add 111 to {1,1,-1} to get a(11) = 220.

EXTENSIONS

Edited by N. J. A. Sloane, Mar 31 2021

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proposed

editing

#18 by Andrew Howroyd at Mon Mar 29 12:54:30 EDT 2021

STATUS

editing

proposed

Discussion

Tue Mar 30

00:20

Joerg Arndt: balanced ternary has digit +1, -1, and 0; so some clarifying remark would be useful.

#17 by Kalan Warusa at Sun Mar 28 20:36:49 EDT 2021

COMMENTS

Also sequence A000027 written in base 3/2.

STATUS

proposed

editing

#16 by Jon E. Schoenfield at Sun Mar 28 20:04:06 EDT 2021

STATUS

editing

proposed

Discussion

Sun Mar 28

20:08

Andrew Howroyd: A024629. Good find. My guess Jon, is that the new comment is erroneous

20:12

Jon E. Schoenfield: That was my guess, too, but I was hoping my guess was wrong....  ?:-/

20:36

Kalan Warusa: Oh. I just realized that my comment is erroneous. Please discard that.

#15 by Jon E. Schoenfield at Sun Mar 28 19:57:15 EDT 2021

CROSSREFS

Cf. A024629.

STATUS

proposed

editing

Discussion

Sun Mar 28

20:02

Andrew Howroyd: I don't anything about fractional bases. I was just going to make a recommendation to say 'n+1' rather than A000027. (assuming a(0) = 1 is the base 3/2 representation of 1).

20:04

Jon E. Schoenfield: Other than the "0" as the first term there, this sequence first differs from A024629 (whose Name field shows "n written in fractional base 3/2") at the first 3-digit term in the Data.  Here, it's "200"; there, it's "210".  All I know about fractional bases is what I've read in the last few minutes, but I can see (given the Formula entry at A024629) how 6 would be "210" in base 3/2.  Is there some other system, also referred to as "base 3/2", in which 6 would be "200"?

20:05

Andrew Howroyd: I think the offset of this sequence is correct. a(2) = 20 = 3 + (-1).

#14 by Jon E. Schoenfield at Sun Mar 28 19:47:09 EDT 2021

STATUS

editing

proposed

Discussion

Sun Mar 28

19:53

Jon E. Schoenfield: Should this sequence's Offset be 1 rather than 0?

19:55

Jon E. Schoenfield: @Andrew -- does this discrepancy relate to the "Variants of Base 3 over 2" paper in a link at A024629?

19:55

Jon E. Schoenfield: Maybe not.  Please disregard.

#13 by Jon E. Schoenfield at Sun Mar 28 19:47:06 EDT 2021

CROSSREFS

Cf. A024629.

STATUS

proposed

editing