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A322510
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a(1) = 0, and for any n > 0, a(2*n) = a(n) + k(n) and a(2*n+1) = a(n) - k(n) where k(n) is the least positive integer not leading to a duplicate term in sequence a.
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5
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0, 1, -1, 4, -2, 2, -4, 5, 3, 6, -10, 7, -3, 8, -16, 15, -5, 12, -6, 19, -7, -9, -11, 22, -8, 9, -15, 28, -12, -14, -18, 16, 14, 10, -20, 13, 11, 17, -29, 20, 18, 21, -35, 23, -41, 24, -46, 57, -13, 26, -42, 35, -17, 25, -55, 29, 27, 30, -54, 31, -59, 32, -68
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OFFSET
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1,4
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COMMENTS
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The point is that the same k(n) must be used for both a(2*n) and a(2*n+1). - N. J. A. Sloane, Dec 17 2019
Apparently every signed integer appears in the sequence.
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LINKS
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Rémy Sigrist, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = (a(2*n) + a(2*n+1))/2.
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EXAMPLE
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The first terms, alongside k(n) and associate children, are:
n a(n) k(n) a(2*n) a(2*n+1)
-- ---- ---- ------ --------
1 0 1 1 -1
2 1 3 4 -2
3 -1 3 2 -4
4 4 1 5 3
5 -2 8 6 -10
6 2 5 7 -3
7 -4 12 8 -16
8 5 10 15 -5
9 3 9 12 -6
10 6 13 19 -7
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PROG
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(PARI) lista(nn) = my (a=[0], s=Set(0)); for (n=1, ceil(nn/2), for (k=1, oo, if (!setsearch(s, a[n]+k) && !setsearch(s, a[n]-k), a=concat(a, [a[n]+k, a[n]-k]); s=setunion(s, Set([a[n]+k, a[n]-k])); break))); a[1..nn]
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CROSSREFS
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For k(n) see A330337, A330338.
See A305410, A304971 and A322574-A322575 for similar sequences.
Sequence in context: A100854 A194688 A317389 * A021707 A126560 A289762
Adjacent sequences: A322507 A322508 A322509 * A322511 A322512 A322513
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KEYWORD
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sign,look
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AUTHOR
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Rémy Sigrist, Dec 13 2018
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STATUS
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approved
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