A000788: Total number of 1's in binary expansions of 0, ..., n
A000788 ➡️ https://oeis.org/A000788

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A000788.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A000788.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A000788.html

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In the decomposition into weight × level + jump, the Twin Prime Conjecture becomes: "The number of prime numbers with a weight of 3 is infinite"

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A000469: 1 together with products of 2 or more distinct primes
A000469 ➡️ https://oeis.org/A000469

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A000469.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A000469.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A000469.html

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A000452: The greedy sequence of integers which avoids 3-term geometric progressions
A000452 ➡️ https://oeis.org/A000452

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A000452.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A000452.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A000452.html

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We see the fundamental theorem of arithmetic and the sieve of Eratosthenes in the decomposition into weight × level + jump of natural numbers. Applied to prime numbers this decomposition leads to a new classification of primes.

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A000415: Numbers that are the sum of 2 but no fewer nonzero squares
A000415 ➡️ https://oeis.org/A000415

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A000415.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A000415.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A000415.html

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🏀 NBA Final · Apr 15, 2026
Golden State Warriors 126 def. LA Clippers 121

〇 No Prime Scores — neither score is prime.

Overall no-prime rate: 62% (36,720 of 59,231)

LAC has finished with the score 121 50 times previously.
GSW has finished with the score 126 42 times previously.
A final score of 121-126 has occurred 34 times previously.

https://www.nbaprimes.com

#NBA #PrimeNumbers #NBAStats

🏀 NBA Final · Apr 15, 2026
Philadelphia 76ers 109★ def. Orlando Magic 97★

🔢🔢 Double Prime — both scores are prime numbers!

Overall double-prime rate: 4.1% (2,444 of 59,230)
PHI: 4.1% (177 of 4,358) of their games
ORL: 3.6% (112 of 3,114) of their games

PHI has finished with the score 109 125 times previously.
ORL has finished with the score 97 81 times previously.
A final score of 109-97 has occurred 76 times previously.

https://www.nbaprimes.com

#NBA #PrimeNumbers #NBAStats

A000408: Numbers that are the sum of three nonzero squares
A000408 ➡️ https://oeis.org/A000408

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A000408.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A000408.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A000408.html

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My first, favorite and most important sequence, the weights of prime numbers: A117078
We see prime numbers classified by level and by weight on the graph.

A117078: a(n) is the smallest k such that prime(n+1) = prime(n) + (prime(n) mod k), or 0 if no such k exists ➡️ https://oeis.org/A117078

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