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A307337 A fractal septenary sequence: For all n >= 1, underline the term with index n + a(n) + 1; then the two subsequences of underlined terms and of non-underlined terms are both equal to the sequence itself. 9
6, 5, 4, 3, 2, 1, 0, 6, 6, 6, 6, 6, 6, 6, 5, 4, 3, 2, 1, 0, 6, 6, 5, 4, 3, 2, 1, 6, 6, 0, 6, 6, 6, 5, 6, 6, 4, 6, 5, 4, 3, 3, 2, 2, 1, 0, 6, 1, 6, 5, 6, 0, 2, 6, 6, 4, 6, 3, 6, 5, 1, 6, 6, 6, 6, 0, 6, 6, 6, 6, 5, 6, 4, 4, 6, 5, 4, 3, 3, 6, 5, 2, 2, 4, 0, 6, 1, 3, 1, 3, 6, 5, 6, 0, 6, 2, 2, 2, 6, 6, 3, 4, 1, 0, 1, 6, 5, 6, 1, 6, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This is defined to be the lexicographically earliest septenary sequence with the following property:

If a(n) = 0, underline a(n+1); if a(n) = 1, underline a(n+2); if a(n) = 2, underline a(n+3); if a(n) = 3, underline a(n+4); if a(n) = 4, underline a(n+5); if a(n) = 5, underline a(n+6); if a(n) = 6, underline a(n+7). Now, the subsequence of (once or more) underlined terms must be equal to the original sequence (copy #1), and the subsequence of non-underlined terms must also reproduce the original sequence (copy #2).

LINKS

Carole Dubois, Table of n, a(n) for n = 1..2005

EXAMPLE

The sequence starts (6,5,4,3,2,1,0,6,6,6,6,6,6,6,5,4,3,2,1,0,6,6,...)

Instead of underlining terms, we will put parentheses around the terms we want to emphasize:

a(1) = 6 produces parentheses around a(1 + 7 = 8):

6,5,4,3,2,1,0,(6),6,6,6,6,6,6,5,4,3,2,1,0,...

a(2) = 5 produces parentheses around a(2 + 6 = 8), which is now already done. Then,

a(3) = 4 produces parentheses around a(3 + 5 = 8), which is already done. Then,

a(4) = 3 produces parentheses around a(4 + 4 = 8) - already done. Then,

a(5) = 2 produces parentheses around a(5 + 3 = 8) - already done. Then,

a(6) = 1 produces parentheses around a(6 + 2 = 8) - already done. Then,

a(7) = 0 produces parentheses around a(7 + 1 = 8) - already done. Then,

a(8) = 6 produces parentheses around a(8 + 7 = 15):

6,5,4,3,2,1,0,(6),6,6,6,6,6,6,(5),4,3,2,1,0,...

a(9) = 6 produces parentheses around a(9 + 7 = 16):

6,5,4,3,2,1,0,(6),6,6,6,6,6,6,(5),(4),3,2,1,0,...

a(10) = 6 produces parentheses around a(10 + 7 = 17):

6,5,4,3,2,1,0,(6),6,6,6,6,6,6,(5),(4),(3),2,1,0,...

a(11) = 6 produces parentheses around a(11 + 7 = 18):

6,5,4,3,2,1,0,(6),6,6,6,6,6,6,(5),(4),(3),(2),1,0,...

a(12) = 6 produces parentheses around a(12 + 7 = 19):

6,5,4,3,2,1,0,(6),6,6,6,6,6,6,(5),(4),(3),(2),(1),0,...

a(13) = 6 produces parentheses around a(13 + 7 = 20):

6,5,4,3,2,1,0,(6),6,6,6,6,6,6,(5),(4),(3),(2),(1),(0),...

a(14) = 6 produces parentheses around a(14 + 7 = 21):

6,5,4,3,2,1,0,(6),6,6,6,6,6,6,(5),(4),(3),(2),(1),(0),(6)...

a(15) = 5 produces parentheses around a(15 + 6 = 21) - already done. Then,

a(16) = 4 produces parentheses around a(16 + 5 = 21) - already done. Then,

a(17) = 3 produces parentheses around a(17 + 4 = 21) - already done.

Etc.

We see in this small example that the parenthesized terms reproduce the initial sequence:

(6),(5),(4),(3),(2),(1),(0),(6)...

The same is true for the subsequence of non-parenthesized terms:

6, 5, 4, 3, 2, 1, 0, 6, 6, 6, 6, 6, 6,...

CROSSREFS

Cf. A307183 (first binary example of such fractal sequences), A307332 (ternary), A307333 (quaternary), A307335 (quinary), A307336 (senary), A307338 (octal), A307339 (nonary), A307340 (decimal).

Sequence in context: A213014 A022962 A023448 * A031055 A249347 A284805

Adjacent sequences:  A307334 A307335 A307336 * A307338 A307339 A307340

KEYWORD

nonn,base

AUTHOR

Eric Angelini and Carole Dubois, Apr 02 2019

STATUS

approved

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Last modified May 31 15:41 EDT 2020. Contains 334748 sequences. (Running on oeis4.)