The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A159619 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A159619

Slowest increasing sequence beginning with 4 such that n and a(n) are either both evil or both odious.
(history; published version)

#30 by N. J. A. Sloane at Fri Aug 30 06:25:10 EDT 2024

STATUS

proposed

approved

#29 by Amiram Eldar at Fri Aug 30 02:37:23 EDT 2024

STATUS

editing

proposed

#28 by Amiram Eldar at Fri Aug 30 02:18:11 EDT 2024

MATHEMATICA

a[n_] := 2 * n + If[EvenQ[n] || EvenQ[IntegerExponent[n+1, 2]], 3, 2]; Array[a, 100] (* Amiram Eldar, Aug 30 2024 *)

PROG

(PARI) a(n) = 2 * n + if(!(n % 2) || !(valuation(n+1, 2) % 2), 3, 2); \\ Amiram Eldar, Aug 30 2024

STATUS

approved

editing

#27 by Peter Luschny at Fri Nov 19 05:01:46 EST 2021

STATUS

reviewed

approved

#26 by Andrey Zabolotskiy at Fri Nov 19 04:54:19 EST 2021

STATUS

proposed

reviewed

#25 by Michel Marcus at Fri Nov 19 03:10:25 EST 2021

STATUS

editing

proposed

Discussion

Fri Nov 19

03:14

Peter Luschny: Jon, we actually have more important things to do here than chasing your name changes. Will this end soon?

03:33

Jon Maiga: Hi Peter, I think it's only about 10-15 entries left - but feel free to skip my proposals (I am in no hurry). The name change is due to a request from the OEIS.

04:54

Andrey Zabolotskiy: I like the new name, btw. Not sure about the links, but whatever.

#24 by Michel Marcus at Fri Nov 19 03:10:18 EST 2021

LINKS

Hsien-Kuei Hwang, S. Janson, and T.-H. Tsai, <a href="http://140.109.74.92/hk/wp-content/files/2016/12/aat-hhrr-1.pdf">Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2)) + f(ceiling(n/2)) + g(n): theory and applications</a>, Preprint 2016.

Hsien-Kuei Hwang, S. Janson, and T.-H. Tsai, <a href="https://doi.org/10.1145/3127585">Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications</a>, ACM Transactions on Algorithms, 13:4 (2017), #47; DOI: 10.1145/3127585.

Vladimir Shevelev, <a href="httphttps://arXivarxiv.org/abs/0904.2101">Several results on sequences which are similar to the positive integers</a>, arXiv:0904.2101 [math.NT], 2009.

STATUS

proposed

editing

#23 by Jon Maiga at Fri Nov 19 03:06:30 EST 2021

STATUS

editing

proposed

#22 by Jon Maiga at Fri Nov 19 03:03:20 EST 2021

COMMENTS

There is a conjecture arising in sequencedb.net Sequence Machine that a(n) = A026491(2+n)-1. This appears to be true: Here we start from on odious or evil number and apply a minimum number of van-Eck-Transforms (of A171898) to reach a value larger than a(n-1). The Dekking formula in A026491 says that A026491 is essentially a partial sum of the backward van-Eck-Transforms, and in a (vague) manner this seems to match.

LINKS

Jon Maiga, <a href="http://sequencedb.net/s/A159619">Computer-generated formulas for A159619</a>, Sequence Machine.

STATUS

approved

editing

Discussion

Fri Nov 19

03:06

Jon Maiga: Name change, see A347957.

#21 by R. J. Mathar at Thu Jun 24 10:36:22 EDT 2021

STATUS

editing

approved