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A334792
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Let L_0 = (0, 1, 2, ...); for k = 1, 2, ..., L_k is obtained by splitting L_{k-1} into runs of k! terms and reversing even-indexed runs; {a(n)} is the limit of L_k as k tends to infinity.
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1
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0, 1, 3, 2, 4, 5, 10, 11, 9, 8, 6, 7, 12, 13, 15, 14, 16, 17, 22, 23, 21, 20, 18, 19, 43, 42, 44, 45, 47, 46, 41, 40, 38, 39, 37, 36, 31, 30, 32, 33, 35, 34, 29, 28, 26, 27, 25, 24, 48, 49, 51, 50, 52, 53, 58, 59, 57, 56, 54, 55, 60, 61, 63, 62, 64, 65, 70, 71
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OFFSET
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0,3
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COMMENTS
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A003188 can be obtained in the same manner by considering runs of 2^k terms.
A163332 can be obtained in the same manner by considering runs of 3^k terms.
This sequence is a permutation of the nonnegative integers.
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LINKS
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EXAMPLE
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L_0 = (0, 1, 2, 3, 4, 5, ...)
L_1 = (0, 1, 2, 3, 4, 5, ...)
L_2 = (0, 1, 3, 2, 4, 5, ...)
As 5 < k! for k > 2, we have:
- a(0) = 0,
- a(1) = 1,
- a(2) = 3,
- a(3) = 2,
- a(4) = 4,
- a(5) = 5.
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PROG
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(PARI) a(n) = { for (k=1, oo, if (n<k!, while (k, my (q=n\k!, r=n%k!); if (q%2, n=(q+1)*k!-1-r; ); k--); return (n))) }
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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