The Aperiodical 

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Integer Sequence Review Mêlée Hyper-Battle DX 2000 (Bracket 4)

By Christian Lawson-Perfect and David Cushing. Posted July 15, 2013

Last week, A001462 – Golomb’s sequence – booked its place in the final. In retaliation for last week’s palaver, this week Christian has picked all the sequences. Unfortunately, the British Summer is happening today so we’re failing a bit, intellectually.



With that in mind, it’s time for round 4 of…



Here are the rules: we’re judging each sequence on four axes: Aesthetics, Completeness, Explicability, and Novelty. We’re reviewing six sequences each week for four weeks, picking a winner from each. Then, we’ll pick one sequence from the ones we reviewed individually before this thing started, plus a wildcard. Finally, a single sequence will be crowned the Integest Sequence 2013! 

Integer Sequence Review Mêlée Hyper-Battle DX 2000 (Bracket 3)

By Christian Lawson-Perfect and David Cushing. Posted July 8, 2013

Last week, A001220 – the Wieferich primes – booked its place in the final. This week, David has picked six sequences all on his own to form Bracket 3 of…



Here are the rules: we’re judging each sequence on four axes: Aesthetics, Completeness, Explicability, and Novelty. We’re reviewing six sequences each week for four weeks, picking a winner from each. Then, we’ll pick one sequence from the ones we reviewed individually before this thing started, plus a wildcard. Finally, a single sequence will be crowned the Integest Sequence 2013! 

Integer Sequence Review Mêlée Hyper-Battle DX 2000 (Bracket 2)

By Christian Lawson-Perfect and David Cushing. Posted July 1, 2013

Last week A002210, the decimal expansion of Khintchine’s constant, emerged victorious from Bracket 1. Now, get ready for round 2 of…



Here are the rules: we’re judging each sequence on four axes: Aesthetics, Completeness, Explicability, and Novelty. We’re reviewing six sequences each week for four weeks, picking a winner from each. Then, we’ll pick one sequence from the ones we reviewed individually before this thing started, plus a wildcard. Finally, a single sequence will be crowned the Integest Sequence 2013! 

Integer Sequence Review Mêlée Hyper-Battle DX 2000 (Bracket 1)

By Christian Lawson-Perfect and David Cushing. Posted June 24, 2013

After taking a couple of weeks off from reviewing integer sequences, we’ve decided to shake up the format. Prepare yourself for…



We’re going to review six sequences each week for four weeks, picking a winner from each. Then, we’ll pick one sequence from the ones we’ve already reviewed individually, plus a wildcard. Finally, a single sequence will be crowned the Integest Sequence 2013!

We’re still judging each sequence on four axes: Aesthetics, Completeness, Explicability, and Novelty.

Without further ado, here we go!

Integer Sequence Review: A052486

By Christian Lawson-Perfect and David Cushing. Posted June 3, 2013

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.

A052486
Achilles numbers – powerful but imperfect: writing n=product(p_i^e_i) then none of the e_i=1 (i.e. powerful(1)) but the highest common factor of the e_i>1 is 1 (so not perfect powers).

72, 108, 200, 288, 392, 432, 500, 648, 675, 800, 864, 968, 972, 1125, 1152, 1323, 1352, 1372, 1568, 1800, 1944, 2000, 2312, 2592, 2700, 2888, 3087, 3200, 3267, 3456, 3528, 3872, 3888, 4000, 4232, 4500, 4563, 4608, 5000, 5292, 5324, 5400, 5408, 5488, ...

Integer sequence review: A000959

By Christian Lawson-Perfect and David Cushing. Posted May 27, 2013

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.

A000959
Lucky numbers.

1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79, 87, 93, 99, 105, 111, 115, 127, 129, 133, 135, 141, 151, 159, 163, 169, 171, 189, 193, 195, 201, 205, 211, 219, 223, 231, 235, 237, 241, 259, 261, 267, 273, 283, 285, 289, 297, 303, ...

Integer sequence review: A005114

By Christian Lawson-Perfect and David Cushing. Posted May 20, 2013

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, ...