cp's mathem-o-blog

Integer sequence review: A005114

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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’re rating sequences on four axes: Novelty, Aesthetics, Explicability and Completeness.

Following last week’s palaver, we’re going to do our best to be serious this time. Game faces on. David promises there will actually be some maths in this sequence.

A005114
Untouchable numbers: impossible values for sum of aliquot parts of $n$.

2, 5, 52, 88, 96, 120, 124, 146, 162, 188, 206, 210, 216, 238, 246, 248, 262, 268, 276, 288, 290, 292, 304, 306, 322, 324, 326, 336, 342, 372, 406, 408, 426, 430, 448, 472, 474, 498, 516, 518, 520, 530, 540, 552, 556, 562, 576, 584, 612, 624, 626, 628, 658, ...

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Irregulars

Axes to Axes

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In which the intrepid maths-crime-fighting duo of Gale and Beveridge find themselves thrust back to a time before people could do maths properly.

It had been a quiet night at the Aperiodical police station. Apart from a few cases of broken scheduling in Excel formulas – nothing a bit of TIME() in the cells wouldn’t put right – there was nothing.

At 11pm, the phone rang. I looked at Sergeant Gale. Sergeant Gale pointedly looked at the phone, raised an eyebrow, and returned to his sudoku.

“Maths Police, bad graphs department. Constable Beveridge speaking, how can I help?”

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News

MathsJam Conference 2013 – registration now open

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Last year's MathsJam conference. Photo by John Histed

As well as being an excellent monthly pub-based meeting, MathsJam also has an annual conference, which takes place every November. Registration is now open for the 2013 conference, which takes place on 2nd and 3rd November.

MathsJam is an opportunity for like-minded self-confessed maths enthusiasts to get together in a pub and share stuff they like. Puzzles, games, problems, or just anything they think is cool or interesting. The annual conference is a weekend of lightning talks, where you can show or demonstrate something you want to share, followed by lengthy coffee breaks for conversation and socialising. And coffee.

Details about the conference, as well as the chance to register and secure your place, can be found at the MathsJam conference website.

Travels in a Mathematical World

On equivalent forms of the weak Goldbach conjecture

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Harald Helfgott has announced a proof of the odd Goldbach conjecture (also known as the ternary or weak Goldbach conjecture). This is big news. Like a good maths newshound, Christian Perfect promptly wrote this up for The Aperiodical as “All odd integers greater than 7 are the sum of three odd primes!”

Wait, though, there’s a problem. As Relinde Jurrius pointed out on Twitter, the formulation used in the paper abstract was not quite the same.

The ternary Goldbach conjecture, or three-primes problem, asserts that every odd integer $N$ greater than $5$ is the sum of three primes. The present paper proves this conjecture.

The version Christian used makes the assertion using odd primes, whereas the paper abstract only claims “the sum of three primes”. The latter version includes $7$ because $7$ can be written as the sum of three primes, but not odd ones ($7 = 3+2+2$). Certainly, you can see both statements of the weak Goldbach conjecture used (for example, here’s the $\gt 5$ version and here’s the $\gt 7$ version). Are they equivalent?

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