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The email shown in sequences is obsolete...use bill.mceachen@gmail.com

married, 2 kids, control systems engineer, interest in prime numbers, born 1962 live in southwest Virginia USA, BS,MSEE,PE
I will post brief info on the few sequences I have authored on the discussion page here shortly if not already

My Sequences

A129912 June 2007 relates to my main PPP conjecture (primes as f{primorials,primorial products}. This is effectively my mild claim to fame, in that it works to explain the way that the primes are distributed. For clarity I will repeat my original conjecture here:

   Every prime number >2 must have an absolute distance to a sequence entry
 (primorials, primorial products) that is itself prime, aside from the special
 cases prime=2 and those primes immediately adjacent to a sequence entry
 (primorials, primorial products). The property is required but not sufficient
 ...it considers distances no larger than the candidate

Rephrasing, this merely means every odd prime number must either be adjacent to, or a prime distance away from a primorial or primorial product. (the distance will be a prime smaller than the candidate)

The usefulness of the property is evident from the Wikicommons image referenced in the sequence. The normalization is merely -1 to +1, where 0 indicates the closest PPP entry was very close, and +/- 1 indicates the closest PPP entry was as far away as possible. Note that the generation of the entries for A129912 appears related to A071562 in a slightly convoluted way. My website details more about the conjecture, including other independent work by Sokol and Potter. Note OEIS begins the sequence at 1, while I begin it at 2 (this seems to happen a lot, I have given up trying to make sense of it).

See comments on the talk page of the Primorial article here, where a poster says more that appropriate wording is that the offset must be coprime to all of the governing factors of the PPP entries.--Bill McEachen 21:39, 25 December 2010 (UTC)

A117825 May 2006 relates to distance from the Highly Composite Numbers and the nearest prime. This relates to Goldbach's Conjecture, my HCN conjecture (see my website), and Fortune's conjecture. This has an interesting pinplot. I posted an image based on CRG data for first 20K here:svg image

A147517 Nov 2008 relates to the symmetrical primes as a f{A002110, primorials}. Here symmetrical primes means the pair sum to twice the primorial center.

A077287 Aug 2003 concerns a mechanism that generates a lot of prime numbers with very volatile numeric spread (see the OEIS scatterplot). I derived while looking for good prime generators.

A113972 Feb 2006 is a form I derived that yields an interesting sequence of primes, with many hi/lo transitions. The OEIS scatterplot here depicts it:[1]

A156053 Feb 2009 shows the Twin Primes (lower of pair) encountered by the Bernoulli Number denominators. It excludes duplicates, and covers through first the 15000 BN. I have an image posted here [2]

A172069 Jan 2010 merely relates the adjacency of primes to entries of A129912. The OEIS plots here depict it:[3]

A147853 Nov 2008 is a spinoff of A147517 and relates to Goldbach partitions of 2*primorials (A002110), providing a very good spread of Goldbach pairs

A102648 Feb 2005 is just a nice function to generate an interesting spread of values (see OEIS pinplot). It is a simple mechanism to quickly generate prime numbers from a fixed range of small integer seeds in a fairly arbitrary way. The submitted version generates values <=20 but this range is dependent on the gain (100) used. The OEIS plots here depict it: [4]

A156703 Feb 2009 is a nice infinite, diverging sequence that is pretty volatile term-by-term. It is formed from ratios of the integers. All but the 3rd entry appear to contain the digit 5 or 9. I posted an image here [5]

A005846 this relates to a classic eqn for generating primes. I have an image posted here [6]

A184938 this relates to bolt-tightening patterns but the reference was deleted when approved. That reference is 1

A218391 this relates to an observation by John Richardson on distinguishing composites from primes. On its face it would not help practically with primality testing, but I'm thinking.

I cannot think of any other sequence I've entered that is worth discussing or needs any commentary.

Minor observations

A few other sequences that I've interacted with:

A002110 I noted that the xth root of the xth primorial seems to have magnitude on the order of its # factors.

A002182 I noted a(n) often corresponds to P(n,m) = number of permutations of n things taken m at a time.

A158869 I asked whether the pattern of rightmost digits) (1,5,7,7) will continue?

A006562 I noted similarity of plot with A013916

A077287 Here is a plot for kissing number aligned to A129912 entries for correlation (I start the latter at entry=2): [7]

A000849 These entries highly correlate to A147517 as follows:

take adjacent differences of the A147517 entries, and plot the log of those values vs A000849.

The resulting linear fit is Y=Ax+B where Y is the A000849, X =A147517, (A,B)=(1.0451,0.241579).

The fit to the admittedly small dataset is better than 0.9999

For clarity, the X dataset is (5,24,160,1374,15511,...) and Y dataset (10,46,343,3248,42331,...)

The fit yields (9,48,351,3320,41804,...)

A013916

I added a comment about the frequency of primes to the sequence entries. Specifically, the "hit" rate is higher than average, after applying PrimePi with adjust for odd, non multiples of 5 as the baseline. I did the analysis in Gnumeric and can supply that data.--Bill McEachen 06:37, 6 December 2010 (UTC)

I also compared Primepi vs that derived from this sequence, the ratio of which seems to be tending towards 1.5
Specifically, for xample, entry 17 is 132. Primepi(132)=32. rat1=32/132/0.4=0.61
The sum of adjacent primes thru the 17th entry is 13 (primes adjacent to each entry). this value 13/entry ptr=17 is 0.76. I was trying to see how relevant a forecaster for PrimePi the sequence is. I looked at the first 1500 entries only and here is the ratio plot:[8]
--Bill McEachen 04:08, 23 January 2011 (UTC)

OEIS Uses

I continue to find new tie-ins to OEIS for my work. I make use of the prime sets named at [9], and they all appear in OEIS, where anciliary notes are often quite useful.--Bill McEachen 06:40, 6 December 2010 (UTC)

Radix transformations

10. Now unlike hexadecimal or other bases where we use more than 10 numeric characters (like A thru F in hex), we we constrain ourselves to digits 0-9. Then, the sequence, interest xpresses the # bases each number can be xpressed in. The first decrease is at 110, which begins the coverage gap for base 11 between 11^2 and 9*11+10. The interest to me is the local minima seen in the sequence. I can provide Python code to produce the representation for any base (fails if in coverage gap).
The sequence begins 1,1,2,2,2,2,3,3,4 considering only primes radix. The sequence was not accepted into OEIS.

Named prime sets

I have a list of named prime sets: User:Bill McEachen/Named prime sets

Mersenne Numbers

I've submitted a sequence A186283 related to A186253. Very volatile but well-bounded at lower end. I know of the prime power theorem, but will the factor hold for all powers? I also submitted the dual case (2^n+1) as A185343. I thank CRG and TD Noe for their assistance.

Sequences of interest

I like A166448 because of its graph and concept captured. It follows a 2nd-degree polynomial very well. Thru 500 terms I got Y=3.698x^2-231.7x+7484, R^2=0.9999+

I updated the related A166449 with a b-file if you're interested. Charles R Greathouse IV 07:13, 24 February 2011 (UTC)

As CRG et al point out, there is an established power-ln relation involved.