%I A133576
%S A133576 4,6,8,9,10,12,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,
%T A133576 33,34,35,36,37,38,39,40,41,42,43,44,45,46,48,49,50,51,52,53,54,55,56,
%U A133576 57,58,59,60,62,63,64,65,66,67,68,69,70,71,72,74,75,76,77,78,79,80,81
%N A133576 Numbers which are sums of consecutive composites.
%C A133576 This is to composites A002808 as A034707 is to primes A000040. The complement 
               of this sequence, numbers which are not sums of consecutive composites, 
               begins 1, 2, 3, 5, 7, 11, 13, 47, 61, 73.
%F A133576 a(n) = SUM[i=j..k] A002808(i).
%e A133576 Every composite is in this sequence as one consecutive composite. We 
               account for primes thus:
%e A133576 a(10) = 17 = 8 + 9.
%e A133576 a(12) = 19 = 9 + 10.
%e A133576 a(16) = 23 = 6 + 8 + 9.
%e A133576 a(22) = 29 = 14 + 15.
%e A133576 a(24) = 31 = 9 + 10 + 12.
%e A133576 a(30) = 37 = 4 + 6 + 8 + 9 + 10.
%e A133576 a(34) = 41 = 20 + 21 = 12 + 14 + 15.
%e A133576 a(36) = 43 = 21 + 22.
%e A133576 Not included = 47.
%e A133576 a(45) = 53 = 26 + 27 = 8 + 9 + 10 + 12 + 14.
%e A133576 a(51) = 59 = 18 + 20 + 21 = 6 + 8 + 9 + 10 + 12 + 14.
%e A133576 Not included = 61.
%e A133576 a(58) = 67 = 33 + 34 = 21 + 22 + 24 = 10 + 12 + 14 + 15 + 16.
%e A133576 a(62) = 71 = 35 + 36 = 22 + 24 + 25 = 4 + 6 + 8 + 9 + 10 + 12 + 14.
%e A133576 Not included = 73.
%e A133576 a(69) = 79 = 39 + 40.
%e A133576 a(73) = 83 = 14 + 15 + 16 + 18 + 20.
%e A133576 a(79) = 89 = 44 + 45.
%e A133576 a(87) = 97 = 48 + 49 = 22 + 24 + 25 + 26.
%e A133576 a(91) = 101 = 50 + 51.
%e A133576 a(93) = 103 = 51 + 52.
%Y A133576 Cf. A002808, A034707.
%Y A133576 Sequence in context: A104499 A137353 A167376 this_sequence A088224 A002808 
               A018252
%Y A133576 Adjacent sequences: A133573 A133574 A133575 this_sequence A133577 A133578 
               A133579
%K A133576 easy,nonn
%O A133576 1,1
%A A133576 Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 26 2007