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A330779
Lexicographically earliest sequence of positive integers such that for any v > 0, the value v appears up to v times, and the associate function f defined by f(n) = Sum_{k = 1..n} a(k) * i^k for n >= 0 is injective (where i denotes the imaginary unit).
4
1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 4, 6, 5, 5, 6, 5, 5, 7, 6, 6, 7, 6, 6, 8, 7, 7, 7, 8, 7, 7, 8, 8, 8, 10, 9, 8, 8, 9, 8, 10, 10, 9, 11, 9, 9, 11, 9, 9, 10, 9, 9, 12, 10, 11, 11, 11, 12, 10, 13, 10, 10, 13, 10, 10, 12, 11, 11, 12, 11, 11, 11, 14, 11, 13, 12, 13
OFFSET
1,2
COMMENTS
The variant of this sequence where each value can only appear up to once, twice or three times corresponds to A000027, A008619 and A008620 respectively.
Graphically, the representation of f resembles a windmill; the variant of f where we allow the value v to appear 3*v times resembles a butterfly (see illustrations in Links section).
EXAMPLE
The first terms, alongside the corresponding values of f(n), are:
n a(n) f(n)
-- ---- ------
0 N/A 0
1 1 i
2 2 -2+i
3 2 -2-i
4 3 1-i
5 3 1+2*i
6 3 -2+2*i
7 4 -2-2*i
8 4 2-2*i
9 4 2+2*i
10 5 -3+2*i
11 4 -3-2*i
12 6 3-2*i
See also illustration in Links section.
PROG
(PARI) See Links section.
CROSSREFS
See A331002 and A331003 for the real and imaginary parts of f, respectively.
See A330780 for another variant.
Cf. A000265.
Sequence in context: A091497 A005707 A087828 * A366632 A110867 A342010
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Dec 31 2019
STATUS
approved