This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A351329 #11 Feb 07 2022 21:42:54 %S A351329 1,2,3,4,6,8,1,2,10,5,7,3,9,11,12,4,13,14,15,6,8,1,2,10,5,16,18,20,7, %T A351329 22,24,26,3,28,30,32,9,34,36,38,11,12,4,13,14,40,17,19,15,21,23,42,6, %U A351329 25,44,27,8,46,29,31,1,33,35,48,2,37,50,39,10,52,41,43,5,45,47,54,16,49,56,51,18,20,7,22 %N A351329 A fractal-like sequence: erase all triples of adjacent terms that have an even sum; the remaining terms rebuild the starting sequence. %C A351329 This is the lexicographically earliest such sequence starting with a(1) = 1 and showing no duplicate term in any triple to be erased. %C A351329 The sequence is fractal-like as it embeds an infinite number of copies of itself. %C A351329 The sequence was built according to these rules (see, in the Example section, the parenthesization technique): %C A351329 1) no overlapping triple of parentheses; a triple is made of integers X, Y and Z; %C A351329 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 A351329 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 A351329 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 even; %C A351329 5) after a(1) = 1, a(2) = 2 and a(3) = 3, 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 A351329 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). %F A351329 Parentheses are added around each triple of terms that have an even sum: %F A351329 (1, 2, 3), (4, 6, 8), 1, 2, (10, 5, 7), 3, (9, 11, 12), 4, (13, 14, 15), 6, 8, 1, 2, 10, 5, (16, 18, 20), 7, (22, 24, 26), 3, (28, 30, 32), 9, (34, 36, 38), 11, 12, 4, 13, 14, (40, 17, 19), 15, (21, 23, 42), 6, (25, 44, 27), 8, (46, 29, 31), 1, ... %F A351329 Erasing all the parenthesized contents yields %F A351329 (...), (...), 1, 2, (...), 3, (...), 4, (...), 6, 8, 1, 2, 10, 5, (...), 7, (...), 3, (...), 9, (...), 11, 12, 4, 13, 14, (...), 15, (...), 6, (...), 8, (...), 1, ... %F A351329 We see that the remaining terms slowly rebuild the starting sequence. %Y A351329 For other erasing criteria, cf. A303845 (prime by concatenation), A303948 (pair sharing a digit), A274329 (pair summing up to a prime), A351330 (triples having an odd sum). %K A351329 base,nonn %O A351329 1,2 %A A351329 _Eric Angelini_ and _Carole Dubois_, Feb 07 2022