A while ago I was working through the $13$ times table for some boring reason, and I was in the kind of mood to find it really quite vexing that the first digits don’t go $1,2,3,4$. Furthermore, $400 \div 13 \approx 31$, so it takes a long time before you see a 4 at all, and that seemed really unfair.

The Online Encyclopedia of Integer Sequences just keeps on growing: at the end of last month it added its 300,000^{th} entry.
Especially round entry numbers are set aside for particularly nice sequences to mark the passing of major milestones in the encyclopedia’s size; this time, we have four nice sequences starting at A300000. These were sequences that were originally submitted with indexes in the high 200,000s but were bumped up to get the attention associated with passing this milestone.

Hi! I’m Dani Poveda. This is my first post here on The Aperiodical. I’m from Spain, and I’m not a mathematician (I’d love to be one, though). I’m currently studying a Spanish equivalent to HNC in Computer Networking. I’d like to share with you some of my inquiries about some numbers. In this case, about triangular square numbers.

I’ll start at the beginning.

I’ve always loved maths, but I wasn’t aware of the number of YouTube maths channels there were. During the months of February and March 2016, I started following some of them (Brady Haran’s Numberphile, James Grime and Matt Parker among others). On July 13th, Matt published the shortest maths video he has ever made:

Maybe it’s a short video, but it got me truly mired in those numbers, as I’ve loved them since I read The Number Devil when I was 8. I only needed some pens, some paper, my calculator (Casio fx-570ES) and if I needed extra help, my laptop to write some code. And I had that quite near me, as I had just got home from tutoring high school students in maths.

I’ll start explaining now how I focused on this puzzle trying to figure out a solution.

As mentioned previously, the Encyclopedia of Integer Sequences is 50 this year. To celebrate that fact, and to encourage readers to concentrate on filling in the gaps in the missing entries instead of just adding new ones, there’s a \$1,000 prize for the best solution to an open problem posed in an OEIS entry.

The announcement by OEIS creator Neil Sloane seems only to have been published as a PDF, so I’m reproducing it here for everyone’s convenience:

Top chap (and newest Aperiodipal?) Neil Sloane, founder of the Online Encyclopedia of Integer Sequences, wrote in to direct our attention towards a “best new integer sequence” contest being run on the sequence-fans mailing list.

Any sequence submitted between the middle of December and the middle of January is eligible. The winners (of which there will be at least three) will each receive a signed copy of the original 1973 Handbook of Integer Sequences, as well as the highly coveted “nice” keyword on their encyclopedia entries.

If you’ve worked with or used any sequences of integers lately (and let’s face it, you have) you might have looked them up in the OEIS. I’ve used it twice today, and it’s still before 9.30am. As you may have gathered from our extensive banging on about it, we’re huge fans of the Online Encyclopedia of Integer Sequences.

If you have visited their site recently, you might have noticed an extra paragraph of red text near the top – yes, they’re doing a Wikipedia, and asking for their users (which is realistically everyone) to donate so they can keep going. It’s a hugely worthy cause, and here at the Aperiodical, we think it’s worth supporting. The OEIS is owned and maintained by The OEIS Foundation Inc., a nonprofit company.

Head over to the OEIS for lists of integers with various properties, and to find out more.

The Online Encyclopedia of Integer Sequences contains over 200,000 sequences. It contains classics, curios, thousands of derivatives entered purely for completeness’s sake, short sequences whose completion would be a huge mathematical achievement, and some entries which are just downright silly.

For a lark, David and I have decided to review some of the Encyclopedia’s sequences. We’ll be rating sequences on four axes: Novelty, Aesthetics, Explicability and Completeness.

A051200
Except for initial term, primes of form “n 3’s followed by 1”.