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Search: id:A133576
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| A133576 |
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Numbers which are sums of consecutive composites. |
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+0
2
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| 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, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 80, 81
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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.
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FORMULA
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a(n) = SUM[i=j..k] A002808(i).
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EXAMPLE
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Every composite is in this sequence as one consecutive composite. We account for primes thus:
a(10) = 17 = 8 + 9.
a(12) = 19 = 9 + 10.
a(16) = 23 = 6 + 8 + 9.
a(22) = 29 = 14 + 15.
a(24) = 31 = 9 + 10 + 12.
a(30) = 37 = 4 + 6 + 8 + 9 + 10.
a(34) = 41 = 20 + 21 = 12 + 14 + 15.
a(36) = 43 = 21 + 22.
Not included = 47.
a(45) = 53 = 26 + 27 = 8 + 9 + 10 + 12 + 14.
a(51) = 59 = 18 + 20 + 21 = 6 + 8 + 9 + 10 + 12 + 14.
Not included = 61.
a(58) = 67 = 33 + 34 = 21 + 22 + 24 = 10 + 12 + 14 + 15 + 16.
a(62) = 71 = 35 + 36 = 22 + 24 + 25 = 4 + 6 + 8 + 9 + 10 + 12 + 14.
Not included = 73.
a(69) = 79 = 39 + 40.
a(73) = 83 = 14 + 15 + 16 + 18 + 20.
a(79) = 89 = 44 + 45.
a(87) = 97 = 48 + 49 = 22 + 24 + 25 + 26.
a(91) = 101 = 50 + 51.
a(93) = 103 = 51 + 52.
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CROSSREFS
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Cf. A002808, A034707.
Sequence in context: A084984 A104499 A137353 this_sequence A088224 A002808 A018252
Adjacent sequences: A133573 A133574 A133575 this_sequence A133577 A133578 A133579
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 26 2007
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