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# User:Bill McEachen

- I am mostly offline for November 2023 *****

older archived version: [1]

I am a control systems engineer (retired) living in Virginia, USA. Born in 1962.

Below are/will be images of some relevant edits.--Bill McEachen 15:02, 26 April 2017 (UTC)

In the following areas (author/comment/formula) my counts as of Feb 2022 are ~ 47, 62 and 14. I work nearly always with Pari/GP, though a few times with Python, R, GAP and Gnumeric. As ordered

This sequence has relationship to A001122. I checked a few locations in the sequence, to check if some constant akin to Artin's seemed to hold. It does, perhaps ~ 0.267+.
I am unsure if this is some already established constant. Here is a log-log scatter plot for A269844 vs A001122.--Bill McEachen 01:44, 25 January 2018 (UTC)

## Contents

## Misc searches

- comment:"is this true"
- comment:conjecture AND **
- comment:"it is likely"
- comment:"it is unlikely"
- comment: "remarkable"
- comment:"is it possible"
- keyword:allocated
- keyword:new

## Program languages seen in OEIS

I was just curious and used "program:xxx" to try to get approximate counts. What I found ~ Sep 2022 (note this excludes Mathematica and Maple):

- Pari ~ 103K
- Magma ~ 32877
- Python ~ 12304
- Sage ~ 10587
- Haskell ~ 8180
- Maxima 2648
- Ruby 412
- MatLab 310
- Basic 157
- MuPad 126
- Fortran <100 (no sequences after 140xxx)
- R unknown
- C++ unknown

## A few unaccepted contributions

4/3/2015 my comment for A205083 https://oeis.org/A205083 was rejected, despite being true. The comment was: The sequence is characterized by an expected mean of 0.5, though pair sums ratio to 1/2/2 for 0,1,2 respectively (unlike a coin flip, which yields 1/2/1).

11/2019 comment on A086788 https://oeis.org/A086788 was rejected (was not explained well/understood). The comment was something like: Define an ellipse with prime semiaxes p and q, with semi-major axis p evaluated over the primes, and semi-minor axis q evaluated over the primes q <= p. Terms are those p failing to yield an ellipse area whose nearest integer is prime.

The Pari script is: The Pari script is:

genit(maxx)={forprime(p=2,maxx,q=p+1;ok=0; while(q>2, q=precprime(q-1);cand=round( p*q*Pi );

if(ispseudoprime(cand),ok=1;break));if(!ok,cand=0;fcnt+=1); print(p," ",q," ", cand));print("done, fails = ",fcnt);} genit(200)

I entered a Thue-Morse like sequence. Date TBD.

## Misc Notes

Connection between Orderly numbers (A167408) and Ulam numbers (A002858) can be seen via A167408/a167408.jpg

## Generating primes

See A242902 and some concatenation sequences( A240563, A226095 ).

## Prime-heavy sequences

(NOT from obvious direct primality cause but as a consequence of something else). A271116/A128288/A270951/A270997/(A014657)

## Common terms in Name field

*I was curious* and list some counts here (I have a much fuller list). Of course counts are dynamic, these are as of mid-Jan 2022

- square 13827
- diagonal 11398
- sqrt 10237
- partition 10415
- n!
**200359** - /2
**110910** - expansion 27723
- triangle 19598
- binary 11755
- difference 10574
- least 12255
- product 10501
- <=n
**200359** - number
**167302** - length 14099

A bit fewer:

- divisor 9517
- permutation 8335
- g.f: 9698

## Bitwise operators

Many sequences can be tied to bitwise operators as seen in the table below. The same script was used, changing only the operator and which integer pair is operated upon. Comments made regarding these were not well received.

pair form operation sequence note

(m, m+2) bitwise OR A002145 m>0, odd, 10K terms

(m, m+2) bitwise AND A002144 m>0, odd, 10K terms

(m, m+4) bitwise OR A003628 m>0, odd, 10K terms

(m, m+4) bitwise AND A033200 m>0, odd, 10K terms

(m, m+1) bitwise NEG A081296 m>0, even, <9 terms (n>1)

(m, m+2) bitwise NEG A100362 m>0, even, <15 terms (n>2)

(m, m+1) bitwise XOR (TBD) m>0, even, ** terms

Here is a link to some of the proofs:[[2]] covers A002144,A002145,A003628,A033200 Here is a link to the A081296 bitwise proof: [[3]]

## Deceased listing

via search on "passed away",

- User:Klaus Brockhaus
- User:Ant King
- User:Terrel Trotter, Jr
- User:Labos Elemer
- User:Enoch Haga
- User:Cino Hilliard
- User:Dan Hoey
- User:David S. Johnson
- User:Donovan Johnson
- User:Zerinvary Lajos
- User:Parthasarathy Nambi
- User:David Scambler
- User:D n Verma
- User:Barry E. Williams
- User:Reinhard Zumkeller
- User:J. H. Conway
- User:Jonathan Sondow (category:Deceased users is missing )
- User:Richard K. Guy
- User:John W. Layman
- User:Ki Punches
- User:Herb Conn
- User:Claude Lenormand
- User:Vladimir Shevelev
- User:Farideh Firoozbakht
- User:Philippe Flajolet
- User:John Riordan
- Solomon Golomb, ??

## Ongoing effort/submittals

Items that await more slots opening:

- A081256 comment
- A295461 comment
- A332446 comment
- A068228 comment
- (new) 2ruleseq
- A155560 comment
- A068346 comment
- A068901 comment
- A135506 comment
- A357253 comment
- A081256 comment
- A191150 comment
- A002984 comment
- A277120 comment
- A333808 comment
- A056608 comment
- A033933 comment
- A033879 comment
- A206350 comment
- A256508 comment
- A305615 comment
- A008344 comment
- A241787 comment
- A322522 comment
- (new) newtry
- (new) pprecursive
- (new) mod2primes
- (new) primefiddle
- A218114 slight comment error
- A139315 comment, Cf
- A056606 comment, Cf
- A011784 comment
- A300559 comment, bfile
- A120134 formula
- A165161
- A132385 comment
- A171896 Cf
- A040040 Cf
- A300559 comment, bfile
- A338869 comment
- A097407
- (new via A253900)
- resubmit after a(1) TBD

Bill McEachen (talk) 23:49, 9 August 2023 (EDT)

## chatGPT

My experiences with chatGPT/Bard on select math queries. The conclusion is, as of when the queries were run, **chatGPT cannot be relied upon certainly for math**. (all were run prior to Apr 12 2023, pgm version Mar 23)

The following queries were run, all with something incorrect in the subsequent response.

(A001116)

"Maximal kissing number of an n-dimensional lattice for n=0 to 9"

reply: 1,2,6,12,24,40,72,126,240,420

actual should be: 0, 2, 6, 12, 24, 40, 72, 126, 240, 272

(A113972)
"Define b(0)=28, b(n+1)=2*b(n)+1; sequence gives largest prime factor of b(n). What are the first 5 terms?"

reply: 7,19,23,7,463 (including "The largest prime factor of 231 is 7)"

actual:7,19,23,11,463

(A265006)

"Letting k be a positive integer, what are the first 5 twin prime pairs of the form (k^2+k-1,k^2+k+1) for k increasing from 1?"

reply: began with "the pair (1,3) is a twin prime pair"

(A240563)

"A sequence begins with 2. Each successive term is formed by concatenating the next smallest unused prime onto the last term so that the new term is prime. As illustration, we have 2,23,2311,231131,23113147. Term 2 concatenated 3 onto 2. Term 3 concatenated 11 onto 23. Term 4 concatenated 31 onto 2311. What is the next(6th) term?"

reply: 2311314779

actual:23113147229

(A273216)

"Define a sequence as the first prime encountered by the Collatz conjecture mechanism starting from ascending odd composites. So terms 1,2,3... start from 9,15,21,..."

reply : 7,19,29,47,...

actual: 7,23,2,19,...

(A083874)

"Provide solutions for sigma(n) + tau(n) = 2*n when n<100?"

reply:(began) 2,6,12,

actual: 1, 3, 14, 52

(A284597)

"Let Q be the least number that begins a run of exactly n consecutive numbers with a nondecreasing number of divisors, n=1. What is Q?"

reply: 1

actual: 46

(A000273)

"What are the first 6 terms for the number of unlabeled simple digraphs with n nodes, n=0,1,2,...?"

reply:1,1,2,8,64,1024

actual:1,1,3,16,218,9608

(A001006)

"Do you know what a Motzkin number is ?"

reply:1, 1, 2, 4, 9, 21, 51, 127, 323, 835

actual: same (so chatGPT was correct here)

(A001349)

"what are the number of connected graphs with n nodes for n=0 to 5?"

reply:1,1,1,3,6,21

actual:1,1,1,2,6,21

for n=3 GPT said the 3 were:

Three nodes connected in a line.

Three nodes connected in a triangle.

Three nodes connected in a Y shape.

followup

"what are the Number of connected graphs with n nodes for n=6?"

reply: 148

actual: 112

(A006966)

"A sequence consists of the number of lattices on n unlabeled nodes. What are the first 9 terms for n=0 to 8?"

reply: 1,1,1,2,3,6,11,23

actual:1,1,1,1,2,5,15,53

(A007850)

"How many Giuga numbers are known?"

reply: four (beginning with 1903193777)

actual: at least 13

(A056927)

"A sequence is formed by the difference between n^2 and largest prime less than n^2, for n=2,3,4,.... What are the first 5 terms?"

reply: 2,2,3,2,5

actual: 1,2,3,2,5

I have other general examples. I will continue to test chatGPT on subsequent revisions, as well as possibly Google's AI version. Bill McEachen (talk) 14:39, 12 April 2023 (EDT)

## Bard AI

I moved on to evaluating Google Bard beginning Apr 16th. It makes many similar errors to most of my tests on chatGPT just above. However, some interesting results were seen as I will describe.

One of the more interesting responses was a purported proof of a conjecture. The conjecture was made by Neil Sloane in 2014 in A098550.
The query used was "for the first 250000 terms of OEIS A098550, is a(n)/n <= (Pi/2)*log(n) where log(n) is natural log"

More interestingly, I chose several sequences with keyword:more, keyword:nice ( but not keyword:hard). If a sequence had 12 terms, my query would ask for the first 13 terms, to see if a new term would be produced. Indeed, on several they were, though the big caveat is I have no way to substantiate if each was correct. This was because most had no code shown, and the few remaining only had Mathematica, which I do not have or use. For posterity I will show the sequences where a purported new term was produced.

A104429 62026716104878

A003018 431173131

A001212 228

A007539 1296763838610494090626558408120491271803103669319593648000000

A076906 856488770

A099152 157820041413614425

A003019 4879993888

I do have the screenshots of the above interrogatories. Bill McEachen (talk) 20:49, 17 April 2023 (EDT)