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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, ...

Integer sequence review: A051200

By Christian Lawson-Perfect and David Cushing. Posted May 13, 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’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”.

3, 31, 331, 3331, 33331, 333331, 3333331, 33333331, 333333333333333331, 3333333333333333333333333333333333333331, 33333333333333333333333333333333333333333333333331, ...

Integer sequence review: A010727

By Christian Lawson-Perfect and David Cushing. Posted May 7, 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’ll be rating sequences on four axes: Novelty, Aesthetics, Explicability and Completeness.

A010727
Constant sequence: the all 7’s sequence.

7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, ...

Integer sequence review: A225143

By Christian Lawson-Perfect and David Cushing. Posted May 4, 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’ll be rating sequences on four axes: Novelty, Aesthetics, Explicability and Completeness.

A225143
Primes from merging of 10 successive digits in decimal expansion of $\zeta(2)$ or $\frac{\pi^2}{6}$.

9499012067, 4990120679, 3040043189, 1896233719, 2337190679, 9628724687, 2510068721, 8721400547, 9681155879, 5587948903, 7564558769, 9632356367, 3235636709, 3200805163, 4445184059, 3876314227, 2276587939, 1979084773, 9420451591, 9120818099, ...