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 P > 1 not yet present inside another pair of parentheses;
3) always end the content inside a pair of parentheses with the smallest integer R > 1 not yet present inside another pair of parentheses such that the concatenation PR is prime;
4) after a(1) = 1, a(2) = 2, a(3) = 3, always try to extend the sequence with a duplicate > 1 of the oldest term of the sequence not yet duplicated; if this leads to a contradiction, open a new pair of parentheses.
LINKS
Jean-Marc Falcoz, Table of n, a(n) for n = 1..11194
EXAMPLE
Parentheses are added around each pair of terms whose concatenation produces a prime:
1,(2,3),2,(4,7),(5,9),3,2,4,(6,13),(8,11),7,5,(10,19),(12,17),(14,23),(15,31),9,...
Erasing all the parenthesized contents yields
1,(...),2,(...),(...),3,2,4,(....),(....),7,5,(.....),(.....),(.....),(.....),9,...
We see that the remaining terms rebuild the starting sequence.
CROSSREFS
KEYWORD
AUTHOR
Eric Angelini and Jean-Marc Falcoz, May 01 2018
STATUS
approved