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A330780
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).
4
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
OFFSET
1,2
COMMENTS
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)
EXAMPLE
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.
PROG
(PARI) See Links section.
CROSSREFS
See A331004 and A331005 for the real and imaginary parts of f, respectively.
See A330779 for another variant.
Sequence in context: A066490 A156685 A124230 * A090973 A076634 A083277
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Dec 31 2019
STATUS
approved