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A330780
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Lexicographically earliest sequence of positive integers such that for any v > 0, the value v appears up to v^2 times, and the associate function f defined by f(n) = Sum_{k = 1..n} a(k) * m(k) for n >= 0 is injective (where {m(k)} corresponds to knight's moves, see Comments for precise definition).
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4
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1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5, 5, 6, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5, 5, 5, 6, 5, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 8, 6, 6, 6, 6, 6, 6, 8, 6, 6, 6, 6, 6, 6, 7
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OFFSET
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1,2
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COMMENTS
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The sequence {m(k)} is 8-periodic:
m(1) = 2 + i,
m(2) = 1 + 2*i, m(3) | m(2)
m(3) = -1 + 2*i, * | *
m(4) = -2 + i, m(4) * | * m(1)
m(5) = -2 - i, ------+------
m(6) = -1 - 2*i, m(5) * | * m(8)
m(7) = 1 - 2*i, * | *
m(8) = 2 - i. m(6) | m(7)
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LINKS
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EXAMPLE
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The first terms, alongside the correspond value of f(n), are:
n a(n) f(n)
-- ---- -------
0 N/A 0
1 1 2+i
2 2 4+5*i
3 2 2+9*i
4 2 -2+11*i
5 2 -6+9*i
6 3 -9+3*i
7 3 -6-3*i
8 3 -6*i
9 3 6-3*i
10 3 9+3*i
11 3 6+9*i
12 3 12*i
See also illustration in Links section.
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PROG
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(PARI) See Links section.
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CROSSREFS
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See A331004 and A331005 for the real and imaginary parts of f, respectively.
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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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