

A162175


Primes classified by weight.


2



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
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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
OEISwiki, 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 A111255 A060213
Adjacent sequences: A162172 A162173 A162174 * A162176 A162177 A162178


KEYWORD

nonn


AUTHOR

Rémi Eismann, Jun 27 2009


STATUS

approved



