cp's OEIS Frontend

A303936 A fractal-like sequence: erasing all pairs of contiguous terms that do not sum up to a prime leaves the sequence unchanged.

%I A303936 #29 Jan 30 2022 19:29:18
%S A303936 1,2,3,4,5,6,8,9,7,4,13,11,12,10,19,14,5,6,17,15,8,9,20,16,7,4,13,18,
%T A303936 21,22,23,24,25,28,26,11,12,29,27,10,19,34,30,31,32,35,33,14,5,6,17,
%U A303936 36,38,15,8,9,20,39,37,16,7,4,13,18,41,40,21,22,45,42,47
%N A303936 A fractal-like sequence: erasing all pairs of contiguous terms that do not sum up to a prime leaves the sequence unchanged.
%C A303936 The sequence is fractal-like as it embeds an infinite number of copies of itself.
%C A303936 The sequence was built according to these rules (see, in the Example section, the parenthesization technique):
%C A303936   1) no overlapping pairs of parentheses;
%C A303936   2) always start the content inside a pair of parentheses with the smallest integer X > 3 not yet present inside another pair of parentheses;
%C A303936   3) always end the content inside a pair of parentheses with the smallest integer Y > 3 not yet present inside another pair of parentheses such that X and Y sum up to a composite number;
%C A303936   4) after a(1) = 1, a(2) = 2 and a(3) = 3, always try to extend the sequence with a duplicate of the oldest term of the sequence not yet duplicated; if this leads to a contradiction, open a new pair of parentheses.
%H A303936 Lars Blomberg, <a href="/A303936/b303936.txt">Table of n, a(n) for n = 1..1000</a>
%e A303936 Parentheses are added around each pair of terms that don't sum up to a prime:
%e A303936 1, 2, 3, (4,5), (6,8), (9,7), 4, (13,11), (12,10), (19,14), 5, 6, (17,15), 8, 9, (20,16), 7, 4, 13,
%e A303936 Erasing all the parenthesized contents yields
%e A303936 1, 2, 3, (...), (...), (...), 4, (.....), (.....), (.....), 5, 6, (.....), 8, 9, (.....), 7, 4, 13,
%e A303936 We see that the remaining terms slowly rebuild the starting sequence.
%Y A303936 For other erasing criteria, cf. A303845 (prime by concatenation), A303948 (pair sharing a digit), A274329 (pair summing up to a prime), A302389 (pair having no digit in common).
%K A303936 nonn
%O A303936 1,2
%A A303936 _Eric Angelini_, May 03 2018