A162174 Primes classified by level.

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

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