A010784: Numbers with distinct decimal digits
A010784 ➡️ https://oeis.org/A010784

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My data have not been verified but my work is highly reproducible.
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- Algorithms ➡️ https://oeis.org/wiki/Decomposition_into_weight_*_level_%2B_jump#Algorithms

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A010061: Binary self or Colombian numbers: numbers that cannot be expressed as the sum of distinct terms of the form 2^k+1 (k>=0), or equivalently, numbers not of form m + sum of binary digits of m.
A010061 ➡️ https://oeis.org/A010061

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A009177: Numbers that are the hypotenuses of more than one Pythagorean triangle
A009177 ➡️ https://oeis.org/A009177

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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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A009112: Areas of Pythagorean triangles: numbers which can be the area of a right triangle with integer sides
A009112 ➡️ https://oeis.org/A009112

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A008917: Numbers that are the sum of 3 positive cubes in more than one way
A008917 ➡️ https://oeis.org/A008917

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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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A008864: a(n) = prime(n) + 1
A008864 ➡️ https://oeis.org/A008864

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A008851: Congruent to 0 or 1 mod 5
A008851 ➡️ https://oeis.org/A008851

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