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Integer sequence review: A225143

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 ζ(2) or π26.

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

Straight away, we can say that this sequence is finite. We’ll deduct a point at the end for that.

Novelty

David: It’s too contrived.

Christian: It’s both the decimal expansion of a famous constant, and a subset of the primes; both well-trodden boulevards of sequence cultivation. Taking just 10 digits shows a lack of imagination.

David: It’s stupid.

Christian: Agreed.

25

Aesthetics

graph

Christian: Look at that! It’s basically random.

David: Sequences should increase. It’s ugly.

Christian: It doesn’t look like proper numbers. It looks like a code. If I was taking any number of digits, I’d want it to be odd.

David: It goes up and down too much. It’s ugly.

Christian: It would look nice if you wrote it in a grid.

David: At least it’s consistent.

25

Explicability

Christian: Pretty straight-forward. The primes are the primes; ζ(s)=n=1ns is the Riemann zeta function. ζ(2) is the sum of the reciprocals of the square numbers, which is π26 thanks to Euler. Write it out in decimal, look for primes. Easy.

David: It’s straight-forward to understand, but what on Earth is the point in it? Why? I’d be happy to give it a 3.

Christian: I think it’s worth a 4.

David: Fine.

45

Completeness

Christian: It’s finite. So it can be completed. The OEIS currently only has the first 1,000 entries. Poor show.

David: Will it contain all the 10-digit primes?!

Christian: It can be completed but it isn’t. What do we think?

35(unsure)

Final score

Deducting, as promised, one point for being loathsomely finite:

2+2+4+320120=1020=12

Looks like this is a pretty average sequence.

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