5 ms·
The claim is that using N numbers per square will result in the pattern holding for N rows, for arbitrarily large N.
by _rpd 8y ago
The claim is that using N numbers per square will result in the pattern holding for N rows, for arbitrarily large N.
- anderskaseorg 8y agoEven if I’m misunderstanding how this is supposed to work for odd n, this claim fails for plenty of even n. n = 14: fails on row 13, col 3 n = 20: fails on row 17, col 8 n = 30: fails on row 17, col 7 n = 38: fails on row 37, col 8 n = 44: fails on row 31, col 2 n = 50: fails on row 43, col 13 …
- _rpd 8y agoThose are some pretty basic checks to miss. Perhaps I've misread OP's claim.
- Recursing 8y agoI think OP is a bit confused, the post is very ambiguous and on telegram he added more info but still hasn't fully formalized what he's trying to say
- shaunxcode 8y agoOP here - really it’s just a matter of I found a cool thing and wanted others ideas/input. I never had a pretense of a proof or a formalization just a cool pattern that emerges from folding the Ulam Spiral up a certain way. I think we were over zealous in the gcd triangle being an exact correspondence now as it clearly is not for some cells.
- airesearcher 8y agoThe pattern does not exactly match GCD as it turns out - but that makes it more curious actually. Here is the Mathematica code that does work for other values. Https://GitHub.com/shaunxcode/a-pattern-in-the-primes
- bustadjustme 8y agoFrom OP: > Interestingly, this same pattern holds for more numbers, and for different intervals. He's not claiming it holds for _all_ n, just for _many_ n.
- shaunxcode 8y agoI think you may misunderstand what terms are in a cell. For instance in your first example what numbers live there? In that observable you can run cellToTerms(row,n,binomialCoEfficient2,col) to get the terms. You can then chain .map(isPrime) (for reasonable sizes it is slurping in data to make testing faster). Those fns are there for interactivity I have not gotten around to adding yet.
- anderskaseorg 8y agoI used range(row * (row - 1) // 2 * n + col, row * (row + 1) // 2 * n + col, row) in Python. For n = 14, row = 13, col = 3, this is [1095, 1108, 1121, 1134, 1147, 1160, 1173, 1186, 1199, 1212, 1225, 1238, 1251, 1264] none of which are prime. cellToTerms(13, 14, binomialCoEfficient2, 3) in the observable gives the same list (though no such calls are made when generating the picture).
- shaunxcode 8y agoOk going back to the mathematica version that does it the slower primality testing per terms in cell way I am seeing the deviations meaning the gcd triangle is not an exact match to what we have here.
- airesearcher 8y agoHere is the code on GitHub - it renders it correctly and addresses the issues. Https://GitHub.com/shaunxcode/a-pattern-in-the-primes