OFFSET
1,2
COMMENTS
The sequence is fractal-like as it embeds an infinite number of copies of itself.
The sequence was built according to these rules (see, in the Example section, the parenthesization technique):
1) no overlapping pairs of parentheses;
2) always start the content inside a pair of parentheses with the smallest integer F not yet present inside another pair of parentheses;
3) always end the content inside a pair of parentheses with the smallest integer I not yet present inside another pair of parentheses such that the sum F + I is a Fibonacci number;
4) after a(2) = 2, always try to extend the sequence with a duplicate of the oldest term of the sequence not yet duplicated; if this leads to a contradiction, open a new pair of parentheses.
LINKS
Lars Blomberg, Table of n, a(n) for n = 1..998
EXAMPLE
Parentheses are added around each pair of terms that sum up to a Fibonacci:
(1,2), (4,9), 1, (3,5), 2, 4, (6,7), 9, 1, 3, (8,13), 5, 2, 4, 6, (10,11), 7, 9, 1, 3, 8, (12,22), 13, 5, 2, 4, 6, 10, (14,20), 11, ...
Erasing all the parenthesized contents yields
(...), (...), 1, (...), 2, 4, (...), 9, 1, 3, (....), 5, 2, 4, 6, (.....), 7, 9, 1, 3, 8, (.....), 13, 5, 2, 4, 6, 10, (.....), 11, ...
We see that the remaining terms slowly rebuild the starting sequence.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Eric Angelini and Lars Blomberg, May 03 2018
STATUS
approved