cp's OEIS Frontend

A351330 A fractal-like sequence: erase all triples of contiguous terms that have an odd sum; the remaining terms rebuild the starting sequence.

%I A351330 #6 Feb 07 2022 21:44:16
%S A351330 1,2,4,6,8,3,1,2,5,7,9,4,11,13,15,6,17,19,21,8,3,1,2,5,7,10,23,12,9,
%T A351330 25,14,16,4,18,20,27,11,22,29,24,13,15,6,17,19,26,31,28,21,33,30,32,8,
%U A351330 34,36,35,3,38,37,40,1,39,42,44,2,46,48,41,5,50,43,52,7,45,54,56,10,58,60,47,23,12,9,25,14
%N A351330 A fractal-like sequence: erase all triples of contiguous terms that have an odd sum; the remaining terms rebuild the starting sequence.
%C A351330 This is the lexicographically earliest such sequence starting with a(1) = 1 and showing no duplicate term in any triple to be erased.
%C A351330 The sequence is fractal-like as it embeds an infinite number of copies of itself.
%C A351330 The sequence was built according to these rules (see, in the Example section, the parenthesization technique):
%C A351330   1) no overlapping triple of parentheses; a triple is made of integers X, Y and Z;
%C A351330   2) always start the content inside a pair of parentheses with the smallest integer X > 1 not yet present inside another pair of parentheses and not leading to a contradiction;
%C A351330   3) always follow X with the smallest integer Y > 1 not yet present inside another pair of parentheses and not leading to a contradiction;
%C A351330   4) always end the content inside a pair of parentheses with the smallest integer Z > 1 not yet present inside another pair of parentheses and not leading to a contradiction such that X + Y + Z is odd;
%C A351330   5) after a(1) = 1, a(2) = 2 and a(3) = 4, always try to extend the sequence with a duplicate > 2 of the oldest term of the sequence not yet duplicated; if this leads to a contradiction, open a new pair of parentheses.
%H A351330 Eric Angelini, <a href="http://cinquantesignes.blogspot.com/2022/01/fabriquons-une-suite-fractale.html">Fabriquons une suite fractale</a>, January 22nd 2022, personal blog (in French).
%e A351330 Parentheses are added around each triple of terms that have an odd sum:
%e A351330 (1, 2, 4), (6, 8, 3), 1, 2, (5, 7, 9), 4, (11, 13, 15), 6, (17, 19, 21), 8, 3, 1, 2, 5, 7, (10, 23, 12), 9, (25, 14, 16), 4, (18, 20, 27), 11, (22, 29, 24), 13, 15, 6, 17, 19, (26, 31, 28), 21, (33, 30, 32), 8, (34, 36, 35), 3, (38, 37, 40), 1, (39, 42, 44), 2,...
%e A351330 Erasing all the parenthesized contents yields
%e A351330 (...), (...), 1, 2, (...), 4, (...), 6, (...), 8, 3, 1, 2, 5, 7, (...), 9, (...), 4, (...), 11, (...), 13, 15, 6, 17, 19, (...), 21, (...), 8, (...), 3, (...), 1, (...), 2,...
%e A351330 We see that the remaining terms slowly rebuild the starting sequence.
%Y A351330 For other erasing criteria, cf. A303845 (prime by concatenation), A303948 (pair sharing a digit), A274329 (pair summing up to a prime), A351329 (triples having an even sum).
%K A351330 base,nonn
%O A351330 1,2
%A A351330 _Eric Angelini_ and _Carole Dubois_, Feb 07 2022