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@MartinEscardo
Amazing! My success rate is 60% at most. I'm going to switch to the calculator!
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Peter Luschny
@peterluschny@mathstodon.xyz
mastodon 4.7.2Grandpa, hanging around in the OEIS helping people to get their stuff in.
Love the history of mathematics, computational mathematics, and reverse engineering. Sometimes translate papers by Euler and Riemann.
I entertain myself with hacking and learning new computer languages.
I wish that TeX and CAS merge into one unity, eliminating any 'formula translating system'.
The image in the header is a photograph of some graffiti art that was once on the Berlin Wall.
(See Wikipedia: Berlin Wall.)
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Rant over 0, 1, 2, 3, 4, 5, 6, ...
I'm ashamed of the OEIS for displaying "A007953: Digital sum" first when entering [0, 1, 2, 3, 4, 5, 6, 7, 8] instead of "A001477 The nonnegative integers".
God may have created the integers, but that doesn't make them 'nice' for the OEIS. But the "digsums," as the things in A007953 are called, are! Once again, "base" wins out over non-base.
Make the OEIS mathematically serious again!
Science
6 May 1960
Vol 131, Issue 3410
pp. 1355-1358
Norbert Wiener
Some Moral and Technical Consequences of Automation: As machines learn they may develop unforeseen strategies at rates that baffle their programmers.
It is my thesis that machines can and do transcend some of the limitations of their designers, and that in doing so, they may be both effective and dangerous.
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@W_Lucht@mstdn.social
It was 6 a.m., and my friend called me from Stockholm. He had just gone out to buy milk for his children’s breakfast, but they wouldn’t sell him any, without giving any explanation. He asked me if I knew why. Later that same morning, I realized what was going on. I studied the wind map and drove to Lisbon.
#OEIS #Partitions
https://oeis.org/A334442
https://oeis.org/A334439
How should integer partitions be listed in the OEIS, what offset should the sequences have, and how should the empty partition be handled?
As an example, let's consider A334439: Irregular triangle whose rows are all integer partitions of n sorted first by sum, then by length, ...
This sequence can also be interpreted as the following triangle, whose n-th row is itself a finite triangle with A000041(n) rows.
0
(1)
(2)(11)
(3)(21)(111)
(4)(31)(22)(211)(1111)
(5)(41)(32)(311)(221)(2111)(11111)
The apex of this triangle is the empty partition, which, however, does not appear in the sequence as it is represented in the OEIS.
1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 4, 3, ..
Probably therefore the index was set to 1. However, this is disputed; the original author had set it to 0. Which value do you consider correct? The same applies to A334301 and A334302.
And then there's also A334442: Irregular triangle whose reversed rows are all integer partitions sorted first by sum, then by length, ...
This sequence can also be interpreted as the following triangle:
0
(1)
(2)(11)
(3)(12)(111)
(4)(13)(22)(112)(1111)
(5)(14)(23)(113)(122)(1112)(11111)
Listed as: 1, 2, 1, 1, 3, 1, 2, 1, 1, .
Here, the offset has been set to 0! Do you see any reason to set it differently in this case than in the other three? Or is it clear to you that A334442 has offset 0, and A334439 has offset 1?
[Q 1] Don't you expect the same offset in all cases?
[Q 2] What offset do you expect? 0 or 1?
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What we need now are readable and efficient implementations. The problem is 'hard'.
Manfred Boergens' program is written in Mathematica and is difficult to understand; as Boergens notes, it was not originally intended for publication.
To make things a bit more accessible, I worked with Gemini to write a readable version in Python. It can at least compute the values up to n = 7 in less than a minute.
https://github.com/PeterLuschny/Gists/blob/main/SocialNetworks.ipynb
For larger values of n, however, 'professional' solutions in C++ are required.
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@dronebetter@mathstodon.xyz Please discuss with Hugo. I am on vacation.
Bitcoin’s creator has hidden behind the pseudonym Satoshi Nakamoto for 17 years.
https://www.nytimes.com/2026/04/08/business/bitcoin-satoshi-nakamoto-identity-adam-back.html
