

A162174


Primes classified by level.


17



5, 13, 19, 23, 31, 37, 43, 47, 53, 61, 73, 97, 113, 127, 131, 139, 151, 157, 163, 173, 181, 199, 211, 223, 233, 257, 263, 271, 293, 307, 313, 317, 337, 353, 373, 389, 397, 401, 421, 457, 479, 509, 523, 541, 547, 563, 571, 593, 607, 619, 647, 653, 661, 673, 691
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OFFSET

1,1


COMMENTS

Conjecture : primes classified by level are rarefying among prime numbers.
A000040(n) = 2, 3, 7, A162175(n), a(n) [From Rémi Eismann, Jun 27 2009]


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


FORMULA

If for prime(n), A117078(n) (the weight) > A117563(n) (the level) then prime(n) is classified by level.
If for prime(n), A117078(n) (the weight) <= A117563(n) (the level) and A117078(n) <> 0 then prime(n) is classified by weight. [From Rémi Eismann, Jun 27 2009]


EXAMPLE

For prime(3)=5, A117078(3)=3 > A117563(3)=1 ; prime(3)=5 is classified by level. For prime(172)=1021, A117078(172)=337 > A117563(172)=3 ; prime(172)=1021 is classified by level.


CROSSREFS

Cf. A117078, A117563, A000040.
Cf. A162175. [From Rémi Eismann, Jun 27 2009]
Sequence in context: A067463 A209663 A156111 * A171603 A118915 A084442
Adjacent sequences: A162171 A162172 A162173 * A162175 A162176 A162177


KEYWORD

nonn


AUTHOR

Rémi Eismann, Jun 27 2009


STATUS

approved



