The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A232740 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A232740

a(n) = Number of terms of A232739 which occur between each consecutive terms of A005228, in range A005228(n)..A005228(n+1).
(history; published version)

#12 by Ralf Stephan at Thu Dec 12 03:24:23 EST 2013

STATUS

proposed

approved

#11 by Antti Karttunen at Fri Dec 06 13:36:11 EST 2013

STATUS

editing

proposed

#10 by Antti Karttunen at Fri Dec 06 13:35:12 EST 2013

COMMENTS

Do any other values appear than 1 and 2? The 2's seem to be getting rarer, as zeros correspondingly get rarer in A232750. This has some implications about how the ratio A005228(n)/A232739(n) will develop. Please see also the comments and graph-drawing link in A232739.

See also comments in A232739 and A232750.

STATUS

proposed

editing

#9 by Antti Karttunen at Fri Dec 06 12:32:16 EST 2013

STATUS

editing

proposed

Discussion

Fri Dec 06

13:09

Alonso del Arte: So that these look a little less like chase sequences, the relation to Hofstadter's sequences needs to be made clearer.

13:25

Antti Karttunen: The behaviour of this and A232750 certainly have some correlation with how the ratio 
https://oeis.org/plot2a?name1=A005228&name2=A232739&tform1=untransformed&tform2=untransformed&shift=0&radiop1=ratio&drawlines=true
will develop. (Where A232739 are the iterates of A030124, the complement of A005228).

E.g. in A232750 it is apparently zeros that are getting rarer, so it should be 2's which are getting rarer in this one.
A232753 is just a "tool sequence" for computing this one, and also available for any later use.

#8 by Antti Karttunen at Fri Dec 06 12:15:16 EST 2013

COMMENTS

See comments in A232739 Do any other values appear than 1 and A232750.2?

See also comments in A232739 and A232750.

LINKS

<a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>

Discussion

Fri Dec 06

12:32

Antti Karttunen: Probably there were additional identities between this and A232750 or other related sequences. But I leave this for a review now.

#7 by Antti Karttunen at Fri Dec 06 12:12:43 EST 2013

LINKS

Antti Karttunen, <a href="/A232740/b232740.txt">Table of n, a(n) for n = 1..2009</a>

#6 by Antti Karttunen at Wed Dec 04 12:19:33 EST 2013

COMMENTS

See comments in A232739 and A232750.

LINKS

<a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>

#5 by Antti Karttunen at Wed Dec 04 12:08:22 EST 2013

EXAMPLE

The two sequences begin as:

A005228: 1, 3, 7, 12, 18, 26, 35, 45, 56, 69, 83, 98, 114, 131, 150, 170, ...

A232739: 2, 4,6, 9, 13, 17, 22, 28, 34, 41, 49, 58, 67, 77, 88, 100, 112, 125, 139, 154, 169, 185, ...

Grouping together the terms of A232739 that occur between two successive terms of A232739, we get {2}, {4,6}, {9}, {13,17}, {22}, {28,34}, {41}, {49}, {58,67}, {77}, ... and counting how many terms are in each such group, we get 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, ..., the first terms of this sequence.

#4 by Antti Karttunen at Wed Dec 04 12:01:49 EST 2013

EXAMPLE

A005228: 1,3, 7, 12, 18, 26, 35, 45, 56, 69, 83, 98, 114, 131, 150, 170, ...

A232739: 2, 4,6, 9, 13, 17, 22, 28, 34, 41, 49, 58, 67, 77, 88, 100, 112, 125, 139, 154, 169, 185, ...

#3 by Antti Karttunen at Wed Dec 04 11:25:16 EST 2013

FORMULA

a(n) = A232753(A005228(n+1)) - A232753(A005228(n)).

PROG

(Scheme)

(define (A232740 n) (- (A232753 (A005228 (+ n 1))) (A232753 (A005228 n))))

CROSSREFS

Cf. A005228, A232739, A232750, A232753.