%I #16 Apr 10 2021 16:33:49
%S 11,17,29,41,59,67,71,79,83,89,101,103,107,109,137,149,167,179,191,
%T 193,197,227,229,239,241,251,269,277,281,283,311,331,347,349,359,367,
%U 379,383,409,419,431,433,439,443,449,461,463,467,487,491,499,503,521,557
%N Primes classified by weight.
%C Conjecture: primes classified by level are rarefying among prime numbers.
%C A000040(n) = 2, 3, 7, A162174(n), a(n). - _Rémi Eismann_, Jun 27 2009
%C 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
%H R. Eismann, <a href="/A162175/b162175.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>
%H OEIS Wiki, <a href="https://oeis.org/wiki/Decomposition_into_weight_*_level_%2B_jump">Decomposition into weight * level + jump</a>
%F 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.
%e 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.
%Y Cf. A117078, A117563, A000040, A162174.
%K nonn
%O 1,1
%A _Rémi Eismann_, Jun 27 2009