User talk:Rémy Sigrist

A280172

Michel Marcus said that you have a plot for t(a(n)) = a(n)*(a(n)+1)/2. The top edge of the plot would be linear, but left & right sides of [concave curved] triangles would grow/decrease quadratically, am I right?

— Daniel Forgues 23:36, 20 September 2019 (EDT)

OK - added scatterplot of n -> a(n)*(a(n)+1)/2 to the sequence.

--Rémy Sigrist (talk) 05:51, 21 September 2019 (EDT)

I don't know whether or not the sequence n -> a(n)*(a(n)+1)/2 should have it's own OEIS entry: apart from the interesting plot, does it have other interesting properties? If Neil Sloane considers it should, I'll let you author it, since you computed the terms and drew the plot. — Daniel Forgues 00:24, 26 September 2019 (EDT)

@Remy Sigrist can you add a colored logarithmic scatterplot of the first 10000 terms of the sequence A058077 which is defined as a(n)=binomial(prime(n+1),prime(n))? here is the link : https://oeis.org/A058077 ... thanks in advance!

OK - illustration added.

@Remy Sigrist thank you very much. Did you really meant "colored logarithmic scatterplot of the first 100000 terms" or it is of "the first 10000 terms" as I suggested. Please If you meant 100000 terms can you add to A277341 a colored logarithmic scatterplot of the first 100000 terms of A277341 since the logarithmic scatterplots of the two sequences are so similar to each other. Also can you check if the first 100000 terms of A277341 are distinct and check conjecture 4 in the comments of A277341 up to n<=100000. Thanks in advance.

@Remy Sigrist please see my draft edits to A277341.

A109299

Re: Your Email

The terms of the sequence A109299 are not strictly in increasing order: a(11) = 992250 > a(12) = 105840.

Is this intentional? If so: how is the order of the terms determined?

COMMENTS

A canonical finite permutation on positive integers is a bijective mapping of [n] = {1, ..., n} to itself, counting the empty mapping as a permutation of the empty set.

REFERENCES

Suggested by Franklin T. Adams-Watters

That is very curious. The value for that permutation is correct:

${\text{1:1 2:4 3:3 4:2}}=p_{1}^{1}p_{2}^{4}p_{3}^{3}p_{4}^{2}=2^{1}3^{4}5^{3}7^{2}=992250$

I don't recall why those permutations were called "canonical". Maybe that was part of the "suggestion" by Franklin T. Adams-Watters? If he's around you could ask him, otherwise I'll go searching through old emails or the SeqFan list if I have records that far back. Jon Awbrey (talk) 14:45, 17 September 2021 (EDT)

I found what looks like my original work file for the sequence, where I have the permutations listed in lexicographic order.

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

1 2 3 4  1:1 2:2 3:3 4:4 = 5402250
1 2 4 3  1:1 2:2 3:4 4:3 = 3858750
1 3 2 4  1:1 2:3 3:2 4:4 = 3241350
1 3 4 2  1:1 2:3 3:4 4:2 = 1653750
1 4 2 3  1:1 2:4 3:2 4:3 = 1389150
1 4 3 2  1:1 2:4 3:3 4:2 =  992250

2 1 3 4  1:2 2:1 3:3 4:4 = 3601500
2 1 4 3  1:2 2:1 3:4 4:3 = 2572500
2 3 1 4  1:2 2:3 3:1 4:4 = 1296540
2 3 4 1  1:2 2:3 3:4 4:1 =  472500
2 4 1 3  1:2 2:4 3:1 4:3 =  555660
2 4 3 1  1:2 2:4 3:3 4:1 =  283500

3 1 2 4  1:3 2:1 3:2 4:4 = 1440600
3 1 4 2  1:3 2:1 3:4 4:2 =  735000
3 2 1 4  1:3 2:2 3:1 4:4 =  864360
3 2 4 1  1:3 2:2 3:4 4:1 =  315000
3 4 1 2  1:3 2:4 3:1 4:2 =  158760
3 4 2 1  1:3 2:4 3:2 4:1 =  113400

4 1 2 3  1:4 2:1 3:2 4:3 =  411600
4 1 3 2  1:4 2:1 3:3 4:2 =  294000
4 2 1 3  1:4 2:2 3:1 4:3 =  246960
4 2 3 1  1:4 2:2 3:3 4:1 =  126000
4 3 1 2  1:4 2:3 3:1 4:2 =  105840
4 3 2 1  1:4 2:3 3:2 4:1 =   75600

5 4 3 2 1  174636000 = 1:5 2:4 3:3 4:2 5:1

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

And then I sorted them by primal code values, getting the order in OEIS.

So this begins to look like a simple mental lapse on my part occurring in the process of sorting the values. It looks like it is meant to be a monotone increasing sequence. Jon Awbrey (talk) 15:28, 17 September 2021 (EDT)

Thanks for catching that! I corrected the displays on my workpage.

• User:Jon Awbrey/WORKSPACE#A109299

Jon Awbrey (talk) 06:48, 18 September 2021 (EDT)