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A213063 Balanced numbers (of order one): k-almost primes that are the average of three successive k-almost primes.

%I A213063 #15 May 13 2013 01:54:22
%S A213063 5,34,53,68,86,94,102,122,142,157,171,173,185,188,194,202,204,211,214,
%T A213063 218,245,257,258,262,263,285,289,302,314,321,338,342,358,366,371,373,
%U A213063 394,404,407,413,415,422,429,435,446,471,489,490,493,497,507,513,517,524,535,562
%N A213063 Balanced numbers (of order one): k-almost primes that are the average of three successive k-almost primes.
%C A213063 Balanced numbers of order one: defined by the union of balanced primes A006562, balanced semiprimes A213025, balanced 3-almost primes (68, 102, 171, 188, 245, 258, 285, 338, 366, 404, 429, 435, 507, 524,..), balanced 4-almost primes (204, 342, 490, 513,..),.., balanced k-almost primes - all of order one.
%C A213063 Balanced numbers of order two are 79, 119, 148, 205, 218, 281, 299, 302, 339, 349, 410, 439, 493,.., defined by the union of balanced primes of order two of A082077, balanced semiprimes of order two (119, 205, 218, 299, 302, 339, 493,..), balanced 3-almost primes of order two (148, 410, 604, 609, 642..),.., balanced k-almost primes of order two.
%H A213063 Charles R Greathouse IV, <a href="/A213063/b213063.txt">Table of n, a(n) for n = 1..10000</a>
%o A213063 (PARI) list(lim)={
%o A213063 lim=lim\1+.5;
%o A213063 my(v=List(),L=log(lim)\log(2),left=vector(L),middle=vector(L),t);
%o A213063 for(n=3,2*lim,
%o A213063 t=bigomega(n);
%o A213063 if(t>L,next);
%o A213063 if(middle[t],
%o A213063 if(2*middle[t] == left[t] + n,
%o A213063 if(middle[t] < lim,
%o A213063 listput(v,middle[t])
%o A213063 ,
%o A213063 if(vecmin(middle) > lim, return(vecsort(Vec(v))))
%o A213063 )
%o A213063 );
%o A213063 left[t]=middle[t];
%o A213063 middle[t]=n
%o A213063 ,
%o A213063 if(left[t],middle[t]=n,left[t]=n)
%o A213063 )
%o A213063 )
%o A213063 }; \\ _Charles R Greathouse IV_, Jun 14 2012
%Y A213063 Cf. A001222, A006562, A014612, A014613, A014614, A046306, A046308, A213025.
%K A213063 nonn
%O A213063 1,1
%A A213063 _Gerasimov Sergey_, Jun 03 2012