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 A213063 Balanced numbers (of order one): k-almost primes that are the average of three successive k-almost primes. 1
 5, 34, 53, 68, 86, 94, 102, 122, 142, 157, 171, 173, 185, 188, 194, 202, 204, 211, 214, 218, 245, 257, 258, 262, 263, 285, 289, 302, 314, 321, 338, 342, 358, 366, 371, 373, 394, 404, 407, 413, 415, 422, 429, 435, 446, 471, 489, 490, 493, 497, 507, 513, 517, 524, 535, 562 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. 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. LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 PROG (PARI) list(lim)={ lim=lim\1+.5; my(v=List(), L=log(lim)\log(2), left=vector(L), middle=vector(L), t); for(n=3, 2*lim, t=bigomega(n); if(t>L, next); if(middle[t], if(2*middle[t] == left[t] + n, if(middle[t] < lim, listput(v, middle[t]) , if(vecmin(middle) > lim, return(vecsort(Vec(v)))) ) ); left[t]=middle[t]; middle[t]=n , if(left[t], middle[t]=n, left[t]=n) ) ) }; \\ Charles R Greathouse IV, Jun 14 2012 CROSSREFS Cf. A001222, A006562, A014612, A014613, A014614, A046306, A046308, A213025. Sequence in context: A193325 A256373 A124936 * A268281 A223137 A068560 Adjacent sequences:  A213060 A213061 A213062 * A213064 A213065 A213066 KEYWORD nonn AUTHOR Gerasimov Sergey, Jun 03 2012 STATUS approved

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