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# User:Bill McEachen

older archived version: [1]

**NOTE: I will be unavailable from approx 3/15-5/15/2022 or so.**

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

## Program languages seen in OEIS

I was just curious and used "program:xxx" to try to get approximate counts. What I found ~ June 2017 (note this excludes Mathematica and Maple):

- Pari ~ 60K
- Magma ~ 21500
- Haskell ~ 8125
- Sage 4161
- Maxima 2270
- MatLab 176
- Ruby 165
- Basic 143
- MuPad 120
- 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]]

Here is a link to the Pari scripting: (PENDING)

## A063118

Sequence terms appear to match the positions for the following mechanism. Take an ordered list of the odd integers >1 where gcd(integer,30)==1. Compute the sum of 10 consecutive list values. a(n) for n>3 are the values at which the sum is congruent {0} Mod 150. These values will occur at positions 10+4k, with k an integer>=0, meaning every 4th value of the base list. See the link added for detailed notes for this comment. [[4]] Bill McEachen (talk) 11:00, 13 March 2022 (EDT)