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A334493 a(n) is the "w" part of f(n) = Sum_{k>=0, d_k>0} (1+w)^(d_k-1) * (3+w)^k where Sum_{k>=0} d_k * 7^k is the base 7 representation of n and w = -1/2 + sqrt(-3)/2 is a primitive cube root of unity; sequence A334492 gives "real" parts. 7
0, 0, 1, 1, 0, -1, -1, 1, 1, 2, 2, 1, 0, 0, 3, 3, 4, 4, 3, 2, 2, 2, 2, 3, 3, 2, 1, 1, -1, -1, 0, 0, -1, -2, -2, -3, -3, -2, -2, -3, -4, -4, -2, -2, -1, -1, -2, -3, -3, 5, 5, 6, 6, 5, 4, 4, 6, 6, 7, 7, 6, 5, 5, 8, 8, 9, 9, 8, 7, 7, 7, 7, 8, 8, 7, 6, 6, 4, 4, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,10
COMMENTS
For any Eisenstein integer z = u + v*w (where u and v are integers), we call u the "real" part of z and v the "w" part of z.
This sequence has connections with A316658; here we work with Eisenstein integers, there with Gaussian integers.
It appears that f defines a bijection from the nonnegative integers to the Eisenstein integers.
LINKS
EXAMPLE
The following diagram depicts f(n) for n = 0..13:
"w" axis
\
. . . . . . . .
\ 10 9
\
. . . . . . . .
3 \ 2 11 7 8
\
._____._____._____._____._____._____._____. "real" axis
4 0 \ 1 12 13
\
. . . . . . . .
5 6 \
- f(9) = 4 + 2*w, hence a(9) = 2.
PROG
(PARI) See Links section.
CROSSREFS
Cf. A307012 (equivalent coordinate for a counterclockwise spiral), A316658, A334492.
Sequence in context: A122865 A246656 A352988 * A074080 A359440 A347687
KEYWORD
sign,base,look
AUTHOR
Rémy Sigrist, May 03 2020
STATUS
approved

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Last modified February 21 09:51 EST 2024. Contains 370228 sequences. (Running on oeis4.)