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User:Bill McEachen

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older archived version: [1]

Rsz mceachen profile.png

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)

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 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 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)


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)