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

Author

Rémi Eismann, Jun 27 2009

Keywords

• nonn

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]

Examples

			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.
		

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

Crossrefs

Cf. A117078, A117563, A000040.

Cf. A162175. [From Rémi Eismann, Jun 27 2009]

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]