[seqfan] Re: A happy chat with my favorite AI.

Sat Jan 28 21:18:49 CET 2023

I would imagine that one of the AI's references gives the trajectory "7,
49, 97, 130, 10, 1, 1, ..." separated by a few words from "4, 16, 37, 58,
89, 145, 42, 20, 4, 16,...", just as in this message. It scraped the
numbers and thought it had a sequence. This is just my conjecture, though.

Allan

On Sat, Jan 28, 2023 at 10:40 AM Neil Sloane <njasloane at gmail.com> wrote:

> "7, 49, 97, 130, 10, 1, 1, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16,..." is
> obviously wrong, since it should be   "7, 49, 97, 130, 10, 1, 1, 1, 1,
> ..."  Where did the 4 come from?
>
> Best regards
> Neil
>
> Neil J. A. Sloane, Chairman, OEIS Foundation.
> Also Visiting Scientist, Math. Dept., Rutgers University,
> Email: njasloane at gmail.com
>
>
>
> On Sat, Jan 28, 2023 at 10:05 AM Allan Wechsler <acwacw at gmail.com> wrote:
>
> > This is cool. It's funny how it alternates between coherence and
> > incoherence. You can tell it doesn't really understand what it's saying,
> > but it still provides interesting ideas for investigation.
> >
> > Of course the happy numbers themselves have been in OEIS forever, as
> > A007770. Also of interest in this connection is A003621 (number of steps
> > needed to reach 1 or 4).
> >
> > On Sat, Jan 28, 2023 at 9:30 AM Peter Luschny <peter.luschny at gmail.com>
> > wrote:
> >
> > > This chat took place on 27. Jan. 2023 with YOU, an AI search
> > > engine. YOU gave many more references, the list given at the
> > > end is greatly shortened.
> > >
> > > * There is a database called the Online Encyclopedia of Integer
> > > sequences. Can you give me an interesting sequence from the OEIS?
> > >
> > > ** Sure! One interesting sequence from the OEIS is the Fibonacci
> > > sequence, which is a sequence of numbers where each number is
> > > the sum of the two preceding numbers, starting with 0 and 1.
> > > The Fibonacci sequence looks like this:
> > > 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
> > >
> > > * Thanks. Can you also give me an interesting integer sequence
> > > which is not in the OEIS?
> > >
> > > ** Sure! One interesting sequence that is not in the OEIS is the
> > > Tribonacci sequence, which is a sequence of numbers where each
> > > number is the sum of the three preceding numbers, starting with
> > > 0, 0, and 1. The Tribonacci sequence looks like this:
> > > 0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, ...
> > >
> > > * This is not true. This is sequence A000073 in the OEIS.
> > >
> > > ** That is correct, sequence A000073 is the Tribonacci sequence
> > > and it is indeed in the OEIS.
> > >
> > > * Well then, please give me an interesting integer sequence
> > > which is not in the OEIS.
> > >
> > > ** Sure! One interesting sequence that is not in the OEIS is
> > > the Happy Number sequence, which is a sequence of numbers
> > > where each number is the sum of the squares of the digits
> > > of the preceding number, starting with 7.
> > > The Happy Number sequence looks like this:
> > > 7, 49, 97, 130, 10, 1, 1, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16, ...
> > >
> > > * Indeed, this sequence is not in the OEIS. But why is this
> > > sequence interesting?
> > >
> > > ** The Happy Number sequence is interesting because it is an
> > > example of a mathematical property called the Collatz Conjecture.
> > > The Collatz Conjecture states that no matter which starting
> > > number you choose, the sequence will always eventually reach
> > > the number 1. This sequence is also interesting due to its
> > > unpredictable nature and its ability to generate a seemingly
> > > random pattern of numbers.
> > >
> > > * Can you give me a formula for this sequence?
> > >
> > > ** The Happy Number sequence is based on the following formula:
> > > If si = 1 for some i>=1, then the original integer s0 is said
> > > to be happy [1]. If Si = 4 for some i>=1, then the original
> > > integer s0 is said to be unhappy [1]. Otherwise, define
> > > s{i+1} = \sum{k=0}^m si^2, where m is the number of digits in si.
> > > This formula can be used to determine whether a given number
> > > is happy or unhappy. If the sequence reaches 1, then the number
> > > is said to be happy. If the sequence reaches 4, then the number
> > > is said to be unhappy.
> > >
> > > * Well, can you give me your source of this formula?
> > >
> > > ** The source for the Happy Number Sequence is the work of American
> > > mathematician, Edward Kasner and his nephew, James Newman.
> > > In their book, Mathematics and the Imagination, they described
> > > the "Happy Number" sequence as a sequence of numbers in which
> > > each number is the sum of the squares of its digits.
> > >
> > > * I thought it was Donald Knuth who invented this sequence?
> > >
> > > ** Yes, you are correct. The Happy Number Sequence was invented
> > > by American mathematician Edward Kasner and his nephew James
> > > Newman, although it was popularized by Donald Knuth in his book,
> > > The Art of Computer Programming [1][2].
> > >
> > > * OK, but why is this interesting sequence not in the OEIS?
> > >
> > > ** The Happy Number Sequence is not included in the On-Line
> > > Encyclopedia of Integer Sequences (OEIS) because it is not
> > > considered an integer sequence. The OEIS is a database of
> > > integer sequences, defined as sequences of integers whose
> > > terms either increase or decrease in a fixed, predictable manner.
> > > The Happy Number Sequence does not meet this definition, as
> > > its terms are determined by a complex algorithm and do not
> > > follow a predictable pattern.
> > >
> > >
> > > [1] Happy Number -- from Wolfram MathWorld
> > > https://mathworld.wolfram.com/HappyNumber.html
> > > SEQUENCE function in Excel - auto generate number series
> > >
> > >
> >
> https://www.ablebits.com/office-addins-blog/sequence-function-excel-auto-generate-number-series/
> > > Confirmation Bias & Wason (1960) 2-4-6 Task
> > > http://www.devpsy.org/teaching/method/confirmation_bias.html
> > > Show Me the Science - How to Wash Your Hands | Handwashing ...
> > > https://www.cdc.gov/handwashing/show-me-the-science-handwashing.html
> > > Quiz #2 : Academic Honesty Policy : Academic Honesty : University ...
> > > https://www.rochester.edu/college/honesty/policy/quiz2.html
> > > How to find, highlight and label a data point in Excel scatter plot
> > >
> > >
> >
> https://www.ablebits.com/office-addins-blog/find-data-point-excel-scatter-graph/
> > > [1]. The Computer Scientist Who Can't Stop Telling Stories | Quanta ...
> > >
> > >
> >
> https://www.quantamagazine.org/computer-scientist-donald-knuth-cant-stop-telling-stories-20200416/
> > > [2]. Donald Knuth: Geek of the Week - Simple Talk
> > >
> > >
> >
> https://www.red-gate.com/simple-talk/opinion/geek-of-the-week/donald-knuth-geek-of-the-week/
> > > Mathematical Writing by Donald E. Knuth, Tracy Larrabee, and Paul ...
> > >
> >
> https://jmlr.csail.mit.edu/reviewing-papers/knuth_mathematical_writing.pdf
> > >
> > > --
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> > >
> >
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