A003726: Numbers with no 3 adjacent 1's in binary expansion
A003726 ➡️ https://oeis.org/A003726

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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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A003635: Inconsummate numbers in base 10: no number is this multiple of the sum of its digits (in base 10)
A003635 ➡️ https://oeis.org/A003635

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A003631: Primes congruent to {2, 3} mod 5
A003631 ➡️ https://oeis.org/A003631

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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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A003628: Primes congruent to {5, 7} mod 8
A003628 ➡️ https://oeis.org/A003628

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A003623: Wythoff AB-numbers: floor(floor(n*phi^2)*phi), where phi = (1+sqrt(5))/2
A003623 ➡️ https://oeis.org/A003623

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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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A003601: Numbers j such that the average of the divisors of j is an integer: sigma_0(j) divides sigma_1(j). Alternatively, numbers j such that tau(j) (A000005(j)) divides sigma(j) (A000203(j))
A003601 ➡️ https://oeis.org/A003601

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A003485: Hurwitz-Radon function at powers of 2
A003485 ➡️ https://oeis.org/A003485

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