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#sequences

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Hacker News<p>Inspect ANSI control codes and escape sequences</p><p><a href="https://ansi.tools" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="">ansi.tools</span><span class="invisible"></span></a></p><p><a href="https://mastodon.social/tags/HackerNews" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>HackerNews</span></a> <a href="https://mastodon.social/tags/ANSI" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ANSI</span></a> <a href="https://mastodon.social/tags/Control" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Control</span></a> <a href="https://mastodon.social/tags/Codes" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Codes</span></a> <a href="https://mastodon.social/tags/Escape" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Escape</span></a> <a href="https://mastodon.social/tags/Sequences" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Sequences</span></a> <a href="https://mastodon.social/tags/Programming" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Programming</span></a> <a href="https://mastodon.social/tags/Tools" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Tools</span></a></p>
Rémi Eismann<p>A short story about my decomposition into weight × level + jump. It's a new fundamental theorem of arithmetic and academia is 11 years late.<br>⬇️</p><p><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>decompwlj</span></a> <a href="https://mathstodon.xyz/tags/FundamentalTheoremOfArithmetic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>FundamentalTheoremOfArithmetic</span></a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/maths" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>maths</span></a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathematics</span></a> <a href="https://mathstodon.xyz/tags/sequences" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sequences</span></a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>OEIS</span></a> <a href="https://mathstodon.xyz/tags/NumberTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>NumberTheory</span></a> <a href="https://mathstodon.xyz/tags/PrimeNumbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PrimeNumbers</span></a> <a href="https://mathstodon.xyz/tags/JavaScript" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>JavaScript</span></a> <a href="https://mathstodon.xyz/tags/php" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>php</span></a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graph</span></a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>3D</span></a> <a href="https://mathstodon.xyz/tags/classification" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>classification</span></a> <a href="https://mathstodon.xyz/tags/primes" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>primes</span></a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>threejs</span></a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>webGL</span></a> <a href="https://mathstodon.xyz/tags/integer" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>integer</span></a> <a href="https://mathstodon.xyz/tags/decomposition" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>decomposition</span></a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>numbers</span></a> <a href="https://mathstodon.xyz/tags/theory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>theory</span></a> <a href="https://mathstodon.xyz/tags/equation" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>equation</span></a> <a href="https://mathstodon.xyz/tags/graphs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graphs</span></a> <a href="https://mathstodon.xyz/tags/sieve" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sieve</span></a> <a href="https://mathstodon.xyz/tags/fundamental" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fundamental</span></a> <a href="https://mathstodon.xyz/tags/theorem" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>theorem</span></a> <a href="https://mathstodon.xyz/tags/arithmetic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>arithmetic</span></a> <a href="https://mathstodon.xyz/tags/NSA" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>NSA</span></a> <a href="https://mathstodon.xyz/tags/CIA" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>CIA</span></a> <a href="https://mathstodon.xyz/tags/DGSE" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>DGSE</span></a> <a href="https://mathstodon.xyz/tags/DGSI" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>DGSI</span></a> <a href="https://mathstodon.xyz/tags/Google" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Google</span></a></p>
Fractal Kitty<p>This needs tweaks, but if you want to endlessly add fibonacci numbers...</p><p>Is it endless? </p><p>What is the average score of randomly moving until you lose?</p><p>do you play better when you don't try?</p><p>I might bother to answer these, I might not. </p><p><a href="https://sumfib.com/" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="">sumfib.com/</span><span class="invisible"></span></a></p><p>It should work on mobile other than not having a delay when you hit the end. (I need to figure out how to fix that)</p><p><a href="https://mathstodon.xyz/tags/mathart" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathart</span></a> <a href="https://mathstodon.xyz/tags/creativecoding" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>creativecoding</span></a> <a href="https://mathstodon.xyz/tags/pisano" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>pisano</span></a> <a href="https://mathstodon.xyz/tags/fibonacci" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fibonacci</span></a> <a href="https://mathstodon.xyz/tags/sums" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sums</span></a> <a href="https://mathstodon.xyz/tags/sequences" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sequences</span></a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathematics</span></a> <a href="https://mathstodon.xyz/tags/addingGames" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>addingGames</span></a> <a href="https://mathstodon.xyz/tags/p5js" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>p5js</span></a> <a href="https://mathstodon.xyz/tags/processing" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>processing</span></a></p>
Rémi Eismann<p><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>decompwlj</span></a> ➡️ It's a decomposition of positive integers. The weight is the smallest such that in the Euclidean division of a number by its weight, the remainder is the jump (first difference, gap). The quotient will be the level. So to decompose a(n), we need a(n+1) with a(n+1)&gt;a(n) (strictly increasing sequence), the decomposition is possible if a(n+1)&lt;3/2×a(n) and we have the unique decomposition a(n) = weight × level + jump.</p><p>We see the fundamental theorem of arithmetic and the sieve of Eratosthenes in the decomposition into weight × level + jump of natural numbers. For natural numbers, the weight is the smallest prime factor of (n-1) and the level is the largest proper divisor of (n-1). Natural numbers classified by level are the (primes + 1) and natural numbers classified by weight are the (composites +1).</p><p>For prime numbers, this decomposition led to a new classification of primes. Primes classified by weight follow Legendre conjecture and i conjecture that primes classified by level rarefy. I think this conjecture is very important for the distribution of primes.</p><p>It's easy to see and prove that lesser of twin primes (&gt;3) have a weight of 3. So the twin primes conjecture can be rewritten: there are infinitely many primes that have a weight of 3.</p><p>I am not mathematician so i decompose sequences to promote my vision of numbers. By doing these decompositions, i apply a kind of sieve on each sequences.</p><p>➡️ <a href="https://oeis.org/wiki/Decomposition_into_weight_*_level_%2B_jump" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Decomposition_in</span><span class="invisible">to_weight_*_level_%2B_jump</span></a></p><p><a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/maths" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>maths</span></a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathematics</span></a> <a href="https://mathstodon.xyz/tags/sequences" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sequences</span></a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>OEIS</span></a> <a href="https://mathstodon.xyz/tags/NumberTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>NumberTheory</span></a> <a href="https://mathstodon.xyz/tags/PrimeNumbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PrimeNumbers</span></a> <a href="https://mathstodon.xyz/tags/JavaScript" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>JavaScript</span></a> <a href="https://mathstodon.xyz/tags/php" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>php</span></a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graph</span></a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>3D</span></a> <a href="https://mathstodon.xyz/tags/classification" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>classification</span></a> <a href="https://mathstodon.xyz/tags/primes" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>primes</span></a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>threejs</span></a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>webGL</span></a> <a href="https://mathstodon.xyz/tags/integer" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>integer</span></a> <a href="https://mathstodon.xyz/tags/decomposition" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>decomposition</span></a> <a href="https://mathstodon.xyz/tags/arithmetic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>arithmetic</span></a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>numbers</span></a> <a href="https://mathstodon.xyz/tags/theory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>theory</span></a> <a href="https://mathstodon.xyz/tags/equation" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>equation</span></a> <a href="https://mathstodon.xyz/tags/graphs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graphs</span></a> <a href="https://mathstodon.xyz/tags/sieve" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sieve</span></a> <a href="https://mathstodon.xyz/tags/fundamental" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fundamental</span></a> <a href="https://mathstodon.xyz/tags/theorem" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>theorem</span></a> <a href="https://mathstodon.xyz/tags/arithmetic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>arithmetic</span></a></p>
Jeff Gilchrist<p><a href="https://mstdn.science/tags/Variant" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Variant</span></a> update for <a href="https://mstdn.science/tags/Ontario" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Ontario</span></a>, Canada (May 20, 2023)</p><p>After a bit of a dip down, XBB.1.16 <a href="https://mstdn.science/tags/Arcturus" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Arcturus</span></a> is really taking off now accounting for 20% of <a href="https://mstdn.science/tags/sequences" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sequences</span></a> while XBB.1.9.1 <a href="https://mstdn.science/tags/Hyperion" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Hyperion</span></a> remains level around 5%. XBB.1.5 <a href="https://mstdn.science/tags/Kraken" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Kraken</span></a> no longer has the majority at 38% and dropping.</p><p>The visualization tool for variants was created by <span class="h-card"><a href="https://aus.social/@mike_honey_" class="u-url mention" rel="nofollow noopener" target="_blank">@<span>mike_honey_</span></a></span> </p><p>You can find weekly Ontario stats including <a href="https://mstdn.science/tags/variants" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>variants</span></a> at ( <a href="http://covid.gilchrist.ca/Ontario.html" rel="nofollow noopener" target="_blank"><span class="invisible">http://</span><span class="ellipsis">covid.gilchrist.ca/Ontario.htm</span><span class="invisible">l</span></a> ). 🧵 1/</p>
beSpacific<p>Scientists Unveil a More Diverse <a href="https://newsie.social/tags/HumanGenome" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>HumanGenome</span></a>. The <a href="https://newsie.social/tags/pangenome" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>pangenome</span></a>, which collated <a href="https://newsie.social/tags/genetic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>genetic</span></a> <a href="https://newsie.social/tags/sequences" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sequences</span></a> from 47 people of <a href="https://newsie.social/tags/diverse" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>diverse</span></a> <a href="https://newsie.social/tags/ethnic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ethnic</span></a> backgrounds, could greatly expand the reach of <a href="https://newsie.social/tags/personalized" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>personalized</span></a> <a href="https://newsie.social/tags/medicine" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>medicine</span></a>.<a href="https://www.nytimes.com/2023/05/10/science/pangenome-human-dna-genetics.html" rel="nofollow noopener" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">nytimes.com/2023/05/10/science</span><span class="invisible">/pangenome-human-dna-genetics.html</span></a></p>
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