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Search: id:A108229
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| 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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This is the Lucas number equivalent of "n occurs A000045(n) times" (A072649), which is one of an infinite number of sequences derived from the Self-Counting Sequence [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, ... (A002024)] which consists of 1 copy of 1, 2 copies of 2, 3 copies of 3 and so on. These include Golomb's sequence, also known as Silverman's sequence (A001462) and the like. As with these others, the challenge is to give a surprisingly simple closed-form formula for a(n).
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EXAMPLE
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Because the first few Lucas numbers L(n), for n = 1, 2, 3, ... are 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, the current sequence consists of 1 one, 3 twos, 4 threes, 7 fours, 11 fives, 29 sixes, 47 sevens, 76 eights, 123 nines and so on.
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CROSSREFS
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Cf. A000204, A002024, A001462, A072649.
Sequence in context: A095840 A131343 A089051 this_sequence A023966 A088141 A083291
Adjacent sequences: A108226 A108227 A108228 this_sequence A108230 A108231 A108232
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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), Jul 23 2005
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