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

Sat Jan 28 16:39:48 CET 2023

"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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