A162175 Primes classified by weight.

11, 17, 29, 41, 59, 67, 71, 79, 83, 89, 101, 103, 107, 109, 137, 149, 167, 179, 191, 193, 197, 227, 229, 239, 241, 251, 269, 277, 281, 283, 311, 331, 347, 349, 359, 367, 379, 383, 409, 419, 431, 433, 439, 443, 449, 461, 463, 467, 487, 491, 499, 503, 521, 557

Offset: 1

Author

Rémi Eismann, Jun 27 2009

Keywords

• nonn

Comments

Conjecture: primes classified by level are rarefying among prime numbers.

A000040(n) = 2, 3, 7, A162174(n), a(n). - Rémi Eismann, Jun 27 2009

By definition, primes classified by weight have a prime gap g(n) < sqrt(p(n)) (or more precisely, for primes classified by weight, we have A001223(n) <= sqrt(A118534(n)) - 1 ). So by definition, prime numbers classified by weight follow Legendre's conjecture and Andrica's conjecture - Rémi Eismann, Aug 26 2013

Examples

			For prime(5)=11, A117078(5)=3 <= A117563(5)=3 ; prime(5)=11 is classified by weight. For prime(170)=1013, A117078(170)=19 <= A117563(170)=53 ; prime(170)=1013 is classified by weight.
		

Links

• R. Eismann, Table of n, a(n) for n = 1..10000
• Remi Eismann, Decomposition of natural numbers into weight * level + jump and application to a new classification of prime numbers
• OEIS Wiki, Decomposition into weight * level + jump

Crossrefs

Cf. A117078, A117563, A000040, A162174.

Formula

If for prime(n), A117078(n) (the weight) <= A117563(n) (the level) and A117078(n) <> 0 then prime(n) is classified by weight. If for prime(n), A117078(n) (the weight) > A117563(n) (the level) then prime(n) is classified by level.