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A113880
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Variation on Recaman's sequence utilizing the four basic operations (/ - + *) in that order.
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0
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1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, 42, 63, 41, 18, 432, 407, 381, 354, 326, 297, 267, 236, 204, 171, 137, 102, 66, 29, 67, 28, 68, 27, 69, 26, 70, 115, 161, 114, 162, 113, 163, 112, 60, 3180, 3126, 3071, 3015, 2958, 51, 110, 50, 111, 49
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OFFSET
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1,2
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COMMENTS
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More precisely:
a(n) = a(n-1)/n if a(n-1)/n is integer and not already in the sequence. Else:
a(n) = a(n-1)-n if a(n-1)-n is positive and not already in the sequence. Else:
a(n) = a(n-1)+n if a(n-1)+n is not already in the sequence. Else:
a(n) = a(n-1)*n if a(n-1)*n is not already in the sequence. Else STOP.
In other words, divide if you can, else subtract, else add, else multiply.
By a(1000) there are 3 division steps, 928 subtraction steps, 59 addition steps and 10 multiplication steps. It is unlikely that every number belongs to the sequence since there are many "holes". It is an open question if there are any repetitions after a multiplication step. Can anybody expand the series?
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LINKS
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Table of n, a(n) for n=1..62.
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EXAMPLE
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a(24)=432 because: a(23) = 18.
18/24 is not an integer.
18-24 is negative.
18 + 24 = 42 is already in the sequence
Therefore 18 * 24 = 432.
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CROSSREFS
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Cf. A005132.
Sequence in context: A064387 A064389 A118201 * A171884 A098141 A175458
Adjacent sequences: A113877 A113878 A113879 * A113881 A113882 A113883
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KEYWORD
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nonn
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AUTHOR
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Sergio Pimentel, Jan 27 2006
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STATUS
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approved
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