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A119632
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Lengths of successive runs in A160357, where a run here means a string of alternating terms.
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3
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1, 1, 3, 1, 11, 1, 4, 10, 1, 4, 28, 1, 10, 24, 1, 8, 1, 2, 1, 1, 4, 1, 9, 4, 1, 2, 36, 1, 12, 4, 1, 2, 1, 3, 28, 1, 10, 52, 1, 18, 1, 32, 1, 12, 15, 38, 1, 14, 32, 1, 12, 1, 44, 1, 16, 1, 148, 1, 50, 7, 22, 1, 8, 3, 4, 1, 2, 70, 1, 24, 1, 114, 1, 42, 1, 200, 1, 68, 6, 1, 2, 13
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Gives a highly compressed version of A005132.
The encoding of Recaman's sequence a(n) = A005132 using A119632 is easy - A11963 counts runs of alternating i(n)'s, where i(n) = (a(n)-a(n-1)/n = A160357(n).
Note that i(n) is always +1 or -1. Each run ends when i(n) = i(n+1).
Here is pseudo-code to reconstruct Recaman's sequence from A119632, which we will call I(n):
a(0) = 0
n = 1
i = 1
for k = 1..
for j = 1..I(k) {
a(n) = a(n-1) + n*i
n = n+1
i = -i
}
i = -i
}
The gzipped file attached to A119632 represents the first 1470117206801829 terms of A005132. The longest run of alternating i(n)'s (maximal value found so far in A119632) is 232144588914. There are 64094657 runs encoded in the gzipped file.
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LINKS
| Allan Wilks, Table of n, a(n) for n = 1..100000
Allan Wilks, The first 64094657 terms (gzipped). (A large file. This encodes the first 1470117206801829 terms of A005132!)
Index entries for sequences related to Recaman's sequence
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EXAMPLE
| A160357 begins 1, 1; 1; -1, 1, 1; 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1; 1; -1, 1, -1, -1; 1, -1, 1, -1, 1, -1, 1, -1, 1, 1; 1; ..., where semicolons demark the successive runs.
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CROSSREFS
| Cf. A005132, A160357.
Sequence in context: A095327 A048953 A200652 * A201131 A134761 A166752
Adjacent sequences: A119629 A119630 A119631 * A119633 A119634 A119635
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com) and Allan Wilks (allan(AT)research.att.com), Jun 10 2006
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EXTENSIONS
| Entry expanded by N. J. A. Sloane, Jul 15 2011.
I am having trouble uploading the gzipped file.
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