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Revisions by Albert Mukovskiy (See also Albert Mukovskiy's wiki page)

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

Number of integers of the form (x^4 + y^4) mod 3^n; a(n) = A289559(3^n).
(history; published version)

#27 by Albert Mukovskiy at Fri Dec 22 11:09:15 EST 2023

STATUS

editing

proposed

#26 by Albert Mukovskiy at Fri Dec 22 11:08:23 EST 2023

COMMENTS

It appears that for n > 4: a(n) = 2*3^(n-1) + a(n-4), for . For n < 5: a(n) = 2*3^(n-1) + 1. Conjecture in closed form: a(n) = 2*ceiling(3^(n+3)/80) - 1.

Discussion

Fri Dec 22

11:08

Albert Mukovskiy: Ok. I splitted the sentence in two for clarity.

#24 by Albert Mukovskiy at Tue Dec 19 09:44:01 EST 2023

STATUS

editing

proposed

#23 by Albert Mukovskiy at Tue Dec 19 09:40:02 EST 2023

PROG

(PARI) a(n) = if(n<5, 2*3^(n-1)+1, 2*3^(n-1)+a(n-4));

STATUS

proposed

editing

Discussion

Tue Dec 19

09:42

Albert Mukovskiy: Dear Michel Marcus,
You wrote: > the 2nd pari program is based on a conjecture ?  if yes must be removed.
 Thanks. Done.
You wrote: > the Thomas Scheuerle, Nov 20 2023 formula is a conjecture ?
   It relates this sequence A367484 to A289559 (it is true).

#20 by Albert Mukovskiy at Sun Dec 17 08:08:23 EST 2023

STATUS

editing

proposed

#19 by Albert Mukovskiy at Sun Dec 17 08:08:12 EST 2023

DATA

1, 3, 7, 19, 55, 165, 493, 1477, 4429, 13287, 39859, 119575, 358723, 1076169, 3228505, 9685513, 29056537, 87169611, 261508831, 784526491, 2353579471, 7060738413, 21182215237, 63546645709, 190639937125, 571919811375, 1715759434123, 5147278302367, 15441834907099

KEYWORD

nonn,more

#18 by Albert Mukovskiy at Sat Nov 25 15:44:43 EST 2023

PROG

(PARI) { a(n) = #setbinop((x, y)->Mod(x, 3^n)^4+Mod(y, 3^n)^4, [0..3^n-1]);

(PARI) { a(n) = if(n<5, 2*3^(n-1)+1, 2*3^(n-1)+a(n-4));

Discussion

Tue Nov 28

10:51

Albert Mukovskiy: At the moment it is checked by direct counting up to a(15)=9685513. In few days hopefully I may check a(16), a(17).

10:57

Albert Mukovskiy: Dear Alois P. Heinz,  on Fri Nov 24 You put back a(16)...a(28), which were computed initially based only on conjectured formula.  Do You have any reference justifying the formula or the terms are confirmed by counting. (Few lines poof can also be inserted in the comments section).

Tue Dec 05

12:07

OEIS Server: This sequence has not been edited or commented on for a week
yet is not proposed for review.  If it is ready for review, please
visit https://oeis.org/draft/A367484 and click the button that reads
"These changes are ready for review by an OEIS Editor."

Thanks.
  - The OEIS Server

Tue Dec 12

08:47

Albert Mukovskiy: I hope I can finish the checking of a(16) in a couple of days by direct counting. I cannot do it currently for a(17) since it might take several weeks. Then, I will update the sequence with a(16) and put the keyword "more".

Sun Dec 17

08:07

Albert Mukovskiy: Checked by direct counting up to a(16) .

#17 by Albert Mukovskiy at Fri Nov 24 16:01:58 EST 2023

FORMULA

a(n) = 2*ceiling(3^(n+3)/80)-1. (Conjectured).

STATUS

proposed

editing

Number of nontrivial divisors of n whose arithmetic derivative is coprime to n.
(history; published version)

#15 by Albert Mukovskiy at Fri Nov 24 11:38:49 EST 2023

STATUS

editing

proposed

Discussion

Fri Nov 24

11:50

Michel Marcus: If subsequences are not allowed : where did you see this ??

12:01

Albert Mukovskiy: No, I have not seen it as a rule..
But I think that A367482 is not very interesting as a regular subsequence of A052273, that is why I think it is better to be removed...

15:39

Alois P. Heinz: withdrawn ...

Sum of the arithmetic derivatives of the nontrivial divisors of n whose arithmetic derivative is coprime to n.
(history; published version)

#14 by Albert Mukovskiy at Fri Nov 24 11:38:27 EST 2023

STATUS

editing

proposed

Discussion

Fri Nov 24

11:50

Michel Marcus: If subsequences are not allowed : where did you see this ??

12:02

Albert Mukovskiy: No, I have not seen it as a rule..
But I think that A367483 is not very interesting as a regular subsequence of A155918, that is why I think it is better to be removed...

15:31

Alois P. Heinz: withdrawn ...