The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A342002 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A342002

Čiurlionis sequence: Arithmetic derivative without its inherited divisor applied to the primorial base exp-function: a(n) = A342001(A276086(n)).
(history; published version)

#65 by Michael De Vlieger at Wed May 04 08:33:57 EDT 2022

STATUS

proposed

approved

#64 by Jon E. Schoenfield at Tue May 03 06:49:11 EDT 2022

STATUS

editing

proposed

Discussion

Tue May 03

06:51

Jon E. Schoenfield: (I hadn't noticed the "C" that should've been "Č" until now.)

07:12

Antti Karttunen: I intentionally left one "incorrect variant" "Ciurlionis" to help text searching...

07:14

Antti Karttunen: But actually "Ciurlionis" (without the reverse hat, i.e. caron) occurs in that Wikimedia-url, so that problem is solved.

07:26

Jon E. Schoenfield: I didn't realize that that was intentional. In any case, I'm glad the problem is solved. :-)

#63 by Jon E. Schoenfield at Tue May 03 06:48:47 EDT 2022

COMMENTS

I decided to name this sequence in honor of Lithuanian artist Mikalojus Čiurlionis, 1875 - 1911, as the scatter plot of this sequence reminds me thematically of his work "Pyramid sonata", with similar elements: fractal repetition in different scales and high tension present, discharging as lightning. Like CiurlionisČiurlionis's paintings, this sequence has many variations, see the Formula and Crossrefs sections. - Antti Karttunen, Apr 30 2022

STATUS

proposed

editing

#62 by Jon E. Schoenfield at Sun May 01 16:29:05 EDT 2022

STATUS

editing

proposed

Discussion

Sun May 01

16:31

Jon E. Schoenfield: I've forgotten the rule on that, but I remember the rule in the OEIS (and many other places) about the possessive form of a name ending in "s". :-)  (I'll leave to others the question of the renaming of the sequence.)

Mon May 02

03:03

Antti Karttunen: Bit unwieldy in this case as the surname already ends with s. Also, the sequence was not discovered by Čiurlionis but instead I dedicate it to him. So it's not his, but for him. BTW, we have Fibonacci sequence, not Fibonacci's.

Tue May 03

06:48

Jon E. Schoenfield: I'm not suggesting changing your edit "Čiurlionis sequence" to "Čiurlionis's sequence". I just changed "Ciurlionis' paintings" to "Ciurlionis's paintings" per the rule spelled out explicitly in the Style Sheet: << The possessive of a singular noun is formed by adding an apostrophe and an S, even if the noun ends in S. Write "Lucas's theorem", not "Lucas' theorem" (or perhaps "the Lucas theorem"). This rule is not universally accepted, so when directly quoting material for which the original editor did not abide by it, the quotation should not be altered. >>

#61 by Jon E. Schoenfield at Sun May 01 16:29:02 EDT 2022

COMMENTS

I decided to name this sequence in honor of Lithuanian artist Mikalojus Čiurlionis, 1875 - 1911, as the scatter plot of this sequence reminds me thematically of his work "Pyramid sonata", with similar elements: fractal repetition in different scales and high tension present, discharging as lightning. Like Ciurlionis' s paintings, also this sequence has many variations, see the Formula and Crossrefs sections. - Antti Karttunen, Apr 30 2022

STATUS

proposed

editing

#60 by Antti Karttunen at Sun May 01 13:55:06 EDT 2022

STATUS

editing

proposed

#59 by Antti Karttunen at Sun May 01 13:50:07 EDT 2022

COMMENTS

I decided to name this sequence in honor of Lithuanian artist Mikalojus Čiurlionis, 1875 - 1911, as the scatter plot of this sequence reminds me thematically of his work "Pyramid sonata", with similar elements: fractal repetition in different scales and high electrical tension present, discharging as lightning. Like Ciurlionis' paintings, also this sequence has many variations, see the Formula and Crossrefs sections. - Antti Karttunen, Apr 30 2022

FORMULA

A342007(a(n)) = A342017(n), A129251(a(n)) = A342019(n). - Antti Karttunen, Mar 11 2021

CROSSREFS

Cf. A002110 (positions of 1's), A003415, A003557, A083345, A085731, A276086, A289234, A327860, A328571, A328572, A342001, A342005, A342006, A342016, A342017, A342019, A342022 (rgs-transform), A342417 (Dirichlet inverse, from the term a(1)=1 onward), , A342419, bbA342463 [= a(A329886(n))], A342920 [= a(A108951(n))], A342921 [= a(A276156(n))].

Cf. A342463 [= a(A329886(n))], A342920 [= a(A108951(n))], A342921 [= a(A276156(n))], A342017 [= A342007(a(n))], A342019 [= A129251(a(n))].

Discussion

Sun May 01

13:55

Antti Karttunen: Should I writen "honor Lithuanian artist M." or "honor the Lithuanian artist M." ?

#58 by Antti Karttunen at Sun May 01 13:44:17 EDT 2022

COMMENTS

The terms are essentially the "wild " or "unherited" part" of the arithmetic derivative (A003415) of those natural numbers (A048103) that are not immediately beyond all hope of reaching zero by iteration (as the terms of A100716 are), ordered by the primorial base expansion of n as in A276086. Sequence A342018 shows the positions of the terms here that have just moved to the "no hope" region, while A342019 shows how many prime powers in any term have breached the p^p limit. Note that the results are same as for A327860(n), as the division by "regular part", A328572(n) does not affect the "wild part" of the arithmetic derivative of A276086(n). - Antti Karttunen, Mar 12 2021

I decided to name this sequence in honor of Lithuanian artist Mikalojus Čiurlionis, 1875 - 1911, as the scatter plot of this sequence reminds me thematically of his work "Pyramid sonata", with same kind of thematic similar elements: fractal repetition in different scales and the high electrical tension present, discharging as lightning. Like Ciurlionis' paintings, also this sequence has many variations, see the formula Formula and crossrefs Crossrefs sections. - Antti Karttunen, Apr 30 2022

EXTENSIONS

Sequence renamed as "Čiurlionis sequence" to honor the Lithuanian artist Mikalojus Čiurlionis - Antti Karttunen, Apr 30 2022

#57 by Antti Karttunen at Sun May 01 13:38:20 EDT 2022

EXTENSIONS

Name Sequence renamed as "Čiurlionis sequence" added to the definition to honor the Lithuanian artist Mikalojus Čiurlionis - Antti Karttunen, Apr 30 2022

#56 by Antti Karttunen at Sun May 01 13:37:40 EDT 2022

CROSSREFS

Cf. A166486 (a(n) mod 2, parity of terms, see comment in A327860), A353640 (a(n) mod 4).