%N A fractal-like sequence: erasing all pairs of consecutive terms that produce a prime by concatenation leaves the sequence unchanged.
%C The sequence is fractal-like as it embeds an infinite number of copies of itself.
%C The sequence was built according to these rules (see, in the Example section, the parenthesization technique):
%C 1) no overlapping pairs of parentheses;
%C 2) always start the content inside a pair of parentheses with the smallest integer P > 1 not yet present inside another pair of parentheses;
%C 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;
%C 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.
%H Jean-Marc Falcoz, <a href="/A303845/b303845.txt">Table of n, a(n) for n = 1..11194</a>
%e Parentheses are added around each pair of terms whose concatenation produces a prime:
%e Erasing all the parenthesized contents yields
%e We see that the remaining terms rebuild the starting sequence.
%Y Cf. A000040 (the prime numbers), A303950 (remove parentheses with Fibonacci sum).
%A _Eric Angelini_ and _Jean-Marc Falcoz_, May 01 2018