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

1,1

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

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

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.

Example

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.

Crossrefs

Cf. A117078, A117563, A000040, A162174.

Sequence in context: A166307 A128464 A105170 * A178128 A330410 A111255

Adjacent sequences: A162172 A162173 A162174 * A162176 A162177 A162178

Keyword

nonn

Author

Rémi Eismann, Jun 27 2009

Status

approved