A330779 - OEIS

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).

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

(list; graph; refs; listen; history; text; internal format)

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).

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Illustration of first steps

Rémy Sigrist, Colored representation of f(n) for n = 0..1000000 in the complex plane (where the color is function of n)

Rémy Sigrist, Colored representation of the variant where the value v can appear up to 3*v times

Rémy Sigrist, Colored representation of the variant where the value v can appear up to A000265(v) times

Rémy Sigrist, Colored representation of the variant where the value v can appear up to prime(v) times

Rémy Sigrist, PARI program for A330779

EXAMPLE

The first terms, alongside the corresponding values of f(n), are:

n a(n) f(n)

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