Here are the number of valid sequences of short length satisfying C=2.

Could one cook up an explicit (possibly recursive) formula? How does that compare to the Erathosthene sieve: can we see a valid sequence as an analog of a prime number, and if so can we adapt a proof (say Euclid’s) that there are infinitely many primes to this context?

Since any opposite of a valid sequence is another valid sequence, I’ll list only the first half, the total number N being twice that.

—

*UPDATE:* corrected some errors! Now I think I have the definition of discrepancy right: for a sequence of length L we want, for any given and for any , that .

*UPDATE:* removed last value which was wrong, much more info on the wiki anyway.

—

L=1: N=2

+

L=2: N=2

++

+-

L=3: N=2

++-

+-+

-++

L=4: N=10

+ + – +

+ – + +

– + + +

+ + – –

+ – + –

– + + –

L=5: N=14

+ + – + –

+ – + + –

– + + + –

+ + – – +

+ – + – +

– + + – +

+ – – + +

– + – + +

– – + + +

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