login
Primes classified by level.
17

%I #3 Mar 31 2012 14:42:50

%S 5,13,19,23,31,37,43,47,53,61,73,97,113,127,131,139,151,157,163,173,

%T 181,199,211,223,233,257,263,271,293,307,313,317,337,353,373,389,397,

%U 401,421,457,479,509,523,541,547,563,571,593,607,619,647,653,661,673,691

%N Primes classified by level.

%C Conjecture : primes classified by level are rarefying among prime numbers.

%C A000040(n) = 2, 3, 7, A162175(n), a(n) [From _Rémi Eismann_, Jun 27 2009]

%H R. Eismann, <a href="/A162174/b162174.txt">Table of n, a(n) for n=1,..,10000</a>

%H Remi Eismann, <a href="http://arXiv.org/abs/0711.0865">Decomposition of natural numbers into weight * level + jump and application to a new classification of prime numbers</a>

%F If for prime(n), A117078(n) (the weight) > A117563(n) (the level) then prime(n) is classified by level.

%F 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]

%e 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.

%Y Cf. A117078, A117563, A000040.

%Y Cf. A162175. [From _Rémi Eismann_, Jun 27 2009]

%K nonn

%O 1,1

%A _Rémi Eismann_, Jun 27 2009