Lmst

A105184: Primes that can be written as concatenation of two primes in decimal representation
A105184 ➡️ https://oeis.org/A105184

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A105184.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A105184.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A105184.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #php #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

Decomposition into weight × level + jump of A105184 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A105184 in 2D (log(weight), log(level))

150 sequences decomposed into weight × level + jump in one GIF (log(weight),log(level)):
1000 sequences decomposed on https://decompwlj.com

#decompwlj #math #mathematics #maths #sequence #OEIS #graph #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

A104272: Ramanujan primes R_n: a(n) is the smallest number such that if x >= a(n), then pi(x) - pi(x/2) >= n, where pi(x) is the number of primes <= x
A104272 ➡️ https://oeis.org/A104272

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

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #php #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

Decomposition into weight × level + jump of Ramanujan primes in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of Ramanujan primes in 2D (log(weight), log(level))

A103664: Primes p such that the number of divisors of p-1 is less than the number of divisors of p+1
A103664 ➡️ https://oeis.org/A103664

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A103664.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A103664.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A103664.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #php #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

Decomposition into weight × level + jump of A103664 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A103664 in 2D (log(weight), log(level))

Decomposition into weight × level + jump of prime numbers in 3D, threejs - webGL (log(weight), log(level), log(jump))
➡️ https://decompwlj.com/3Dgraph/Prime_numbers.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #php #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

A102491: Numbers whose base-20 representation can be written with decimal digits

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A102491.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A102491.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A102491.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #php #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

Decomposition into weight × level + jump of A102491 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A102491 in 2D (log(weight), log(level))

A102487: Numbers in base-12 representation that can be written with decimal digits

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A102487.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A102487.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A102487.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #php #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

Decomposition into weight × level + jump of A102487 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A102487 in 2D (log(weight), log(level))

My data have not been verified but my work is highly reproducible.
- Downloads (csv, img, dump) ➡️ https://decompwlj.com/
- Algorithms ➡️ https://oeis.org/wiki/Decomposition_into_weight_*_level_%2B_jump#Algorithms

#decompwlj #math #mathematics #maths #sequence #OEIS #Downloads #Algorithms #numbers #primes #PrimeNumbers #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

Algorithm of the decomposition into weight × level + jump in PARI/GP from the OEIS Wiki

A101594: Numbers with exactly two distinct decimal digits, neither of which is 0

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A101594.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A101594.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A101594.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #php #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

Decomposition into weight × level + jump of A101594 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A101594 in 2D (log(weight), log(level))

Is this an error in the textbook?

I don't think "let 𝑝 be prime" is required.

And none of the online resources state that 𝑝 must be prime eg
https://en.wikipedia.org/wiki/Euclid–Euler_theorem

#numbertheory #maths

euclid-euler theorem - showing possibly unnecessary "let p be prime"

A101082: Numbers n such that binary representation contains bit strings "10" and "01" (possibly overlapping)

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A101082.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A101082.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A101082.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #php #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

Decomposition into weight × level + jump of A101082 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A101082 in 2D (log(weight), log(level))

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.

#decompwlj #math #mathematics #maths #sequence #OEIS #graph #natural #numbers #primes #PrimeNumbers #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #Eratosthenes #fundamental #theorem #arithmetic #research

Decomposition into weight × level + jump of natural numbers: the fundamental theorem of arithmetic and the sieve of Eratosthenes

Graph in 2D (log(weight), log(level)) of the decomposition into weight × level + jump of natural numbers

Decomposition into weight × level + jump of prime numbers: in 2D with sequences on the OEIS: a new classification of primes

Graph in 2D (log(weight), log(level)) of the decomposition into weight × level + jump of prime numbers

A100959: Non-semiprimes

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A100959.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A100959.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A100959.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #php #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

Decomposition into weight × level + jump of non-semiprimes in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of non-semiprimes in 2D (log(weight), log(level))

Do odd perfect numbers exist?

We don't know.

That's a cool open problem!

https://en.wikipedia.org/wiki/Perfect_number#Odd_perfect_numbers

#maths #numbertheory

Now this animation is available for the 1000 sequences decomposed on my website.
Accessible from the 3Dgraph, 2Dgraph500terms and 2dgraphs pages ➡️ https://decompwlj.com
A little more work on axis sizing and controls.

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #php #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research