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 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)
-- ---- ------
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
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Dec 31 2019
STATUS
approved