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%I #22 Jun 04 2018 18:58:01
%S 1,2,3,2,4,7,5,9,3,2,4,6,13,8,11,7,5,10,19,12,17,14,23,15,31,9,3,2,4,
%T 6,16,21,18,47,13,8,20,27,22,37,11,7,5,10,24,41,19,12,25,39,26,33,17,
%U 14,28,43,23,15,29,53,31,9,3,2,4,6,16,30,49,21,18,32,51,34,57,47,13,8,20,35,59,36,71,38,63,27,22,40,73
%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 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,...
%e Erasing all the parenthesized contents yields
%e 1,(...),2,(...),(...),3,2,4,(....),(....),7,5,(.....),(.....),(.....),(.....),9,...
%e We see that the remaining terms rebuild the starting sequence.
%Y Cf. A000040 (the prime numbers), A303950 (remove parentheses with Fibonacci sum).
%K nonn,base,look
%O 1,2
%A _Eric Angelini_ and _Jean-Marc Falcoz_, May 01 2018
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