Lost Brisbane

I noticed a site on Facebook called Lost Brisbane and thought I'd make a post about the house at 21 Mayneview Street where I grew up. It's rather special in that all the houses in the street have been replaced by warehouses and office buildings but my old house, at the top of the hill, still survives. See Figure 1.

Figure 1

I crafted what I thought was a well-worded post with my main point being that, while my childhood home was not lost, the neighbourhood had been. The houses and the people who lived in them had gone, replaced by soulless buildings that, though occupied on a 9 to 5 basis, were deserted at night and on weekends.

Well, that post didn't last long. It was quickly deleted with no reason given. Of course, I'd set myself up for rejection yet again. I was reminded of my encounters with the custodians of the OEIS, Online Encyclopedia of Integer Sequences, who could approve or deny a sequence submission on a whim. Once again, with Lost Brisbane, I was handing someone the power to approve or deny. I won't make that mistake a third time hopefully.

The irony is that I have nothing to do with Facebook and only make use of its associated Messenger service. Occasionally, I'll post an Instagram photo to Facebook as well but that's it. What possessed me to contribute to this Facebook site I don't know. Nostalgia I guess. I thought my house on the hill story was an interesting one and one that could be shared. From now on I'll stick to blog posts that I control and that people can read or not as they see fit.

WordPress Glitches

When choosing a theme for your website, one that will carry over to your WordPress blog, don't choose a dark theme. This has become more and more apparent as I kept posting to my blog. Initially the problem was with the numbering of graphics. Under each graphic, there is the opportunity to insert a caption. The problem with using a dark theme is that the caption uses black text and is therefore invisible. It must be manually changed to white text.

That wasn't too much of an inconvenience, although it was annoying. The problem extended however, to the pasting of text. Copying for example from a sequence of numbers in the OEIS, the pasted text was invisible again because of the black on black problem. Other problems occurred when dealing with mathematical content to the extent that I changed to a white background theme.

I've been unimpressed with BlueHost due its slowness and the problems in accessing it all on occasions. I find the whole experience clunky and frustrating, as if I'm back in the 1990's. It has an irritating retro-feel about it. It's hard to believe that this is the most popular blogging platform. I guess I'll persist with it while my subscription is active but I'll definitely be backing up all my posts to Blogger. The guy in the graphic above doesn't really give any good reasons why people hate bluehost but the picture helps capture my mood.

In the Groove

Sometimes you get into a groove, habits form and you don't go beyond the prescribed limits that you yourself have set. For some years, I've been using the Online Encyclopaedia of Integer Sequences (OEIS) when examining the mathematical significance of the number associated with my diurnal age. Now that my numbered days are approaching 26,000, I long ago realised that I was missing out on some important sequences because the number wasn't listed in the OEIS display.

25406 is a good example of what I mean. This number is a member of OEIS A025414:

a(n) is the smallest number that is the sum of 3 nonzero squares in exactly n ways

3, 27, 54, 129, 194, 209, 341, 374, 614, 594, 854, 1106, 1314, 1154, 1286, 1746, 1634, 1881, 2141, 2246, 2609, 2889, 3461, 3366, 3449, 3506, 4241, 4289, 5066, 4826, 5381, 5606, 6569, 5561, 6254, 7601, 8186, 8069, 8714, 8126, 9434, 8921, 8774, 11066, 11574

Clearly 25406 is well short of making an appearance in the above list. However, it is listed in a Table of n, a(n) for n = 1..1000 where it is the 72nd entrant and thus the smallest number that can be represented as a sum of two nonzero squares in 72 different ways. But how to discover this when a search for 25406 using the OEIS search bar does not bring up this sequence?

The secret was to click on Hints and then reading through the contents of this page, one discovers the following little pearl of wisdom:

To search for a single large number in the OEIS, try Google, because Google has searched all the .txt files in the OEIS, and so may do a better job than the OEIS search engine.

Sure enough, this approach throws up a whole lot of other OEIS results that don't appear in the normal search, among them being OEIS A025414. This is a significant discovery because it increases the likelihood of finding an interesting sequence for large numbers such as 25406. The pedagogical principle at play here is to poke around and don't stay stuck within the same comfortable but limited perimeter. This is what had happened to me with the OEIS searching.

Day 24179

Today I'm 24179 days old and it's a prime day because 24179 is prime. It forms part of a twin prime pair with 24181. It enjoys 16 entries in the OEIS. One of the entries states that it is a member of a sequence of numbers with the property that it is the first member of a twin prime pair whose sum equals the sums of two consecutive smaller pairs of twin primes. The first member of the sequence A225943 is 17 because 17 + 19 = (5 + 7) + (11 + 13). In the case of 24179, we have 24179 + 24181 = 48360 = (12071 + 12073) + (12107 + 12109). That's the most interesting of the entries. It doesn't take too long to discover the smaller primes. Using WolframAlpha, I just searched for primes between 12000 and 12200 and looked at the sums of the various consecutive twin prime pairs.

Reconnecting

I just looked at my previous post, made over a year ago now. I'd forgotten all about my integer equations based on the number of days I'd been alive. Today is day number 23924 and sure enough: $$(2-3) = -9 +(2 \times 4)$$For most of the previous year, I kept a daily blog going at voodooguru.postach.io generated from within a notebook in Evernote. Most the information for each day's number was taken from either WolframAlpha or the Online Encyclopedia of Integer Sequences. During my break in Jakarta I stopped completely; however, I've now resumed but am only tracking my prime days. I needed a break. My next prime day is Wednesday October 8th when I'll be 23929 days old.

23934 by the way is equal to 2 x 2 x 5981 so today my life can be divided exactly into four equal parts each of about 16.375 years duration. So the sequence is 16.375, 32.75, 49.125 and 62.5 (minus a day for each quarter because I'm about four days away from the 62.5 milestone). So sometime in May 1998 I was exactly 75% of my current age.