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%I #8 Mar 12 2019 22:31:10
%S 1,9,3,1,11,2,9,4,3,1,12,5,7,6,8,10,13,14,15,16,18,17,19,20,21,22,11,
%T 23,24,25,26,27,29,28,30,31,2,9,32,33,34,35,36,37,38,40,4,3,1,39,41,
%U 42,43,12,44,45,46,47,48,49,51,52,50,5,53,54,55,57,56,58,59,7,60,6,61,62,63,64,65,67,66,68,69,8,70,72,71,73,74
%N An irregular fractal sequence: underline a(n) iff the sum [a(n-1) + a(n)] is a palindrome; all underlined terms rebuild the starting sequence.
%C The sequence S starts with a(1) = 1 and a(2) = 9. S is extended by duplicating the first term A among the not yet duplicated terms of S, under the condition that the sum [a(n-1) + a(n)] is a palindrome. If this is not the case, we then extend S with the smallest integer X not yet present in S such that the sum [a(n-1) + a(n)] is not a palindrome. S is the lexicographically earliest sequence with this property.
%H Jean-Marc Falcoz, <a href="/A306808/b306808.txt">Table of n, a(n) for n = 1..10002</a>
%e S starts with a(1) = 1 and a(2) = 9
%e Can we duplicate a(1) to form a(3)? No, as a(2) + a(3) would be 10 and 10 is not a palindrome. We thus extend S with the smallest integer X not yet in S such that [a(2) + X] is not a palindrome. We get a(3) = 3.
%e Can we duplicate a(1) to form a(4)? Yes, as a(3) + a(4) = 4, which is a palindrome. We get a(4) = 1.
%e Can we duplicate a(2) to form a(5)? No, as a(4) + a(5) would be 10 and 10 is not a palindrome. We thus extend S with the smallest integer X not yet in S such that [a(4) + X] is not a palindrome; we get a(5) = 11.
%e Can we duplicate a(2) to form a(6)? No, as a(5) + a(6) would be 20 and 20 is not a palindrome. We thus extend S with the smallest integer X not yet in S such that [a(5) + X] is not a palindrome; we get a(6) = 2.
%e Can we duplicate a(2) to form a(7)? Yes, as [a(6) + a(7)] = 11, which is a palindrome. We get a(7) = 9.
%e Etc.
%Y Cf. A306803 (which is obtained by replacing palindrome by prime in the definition).
%K base,nonn,look
%O 1,2
%A _Eric Angelini_ and _Jean-Marc Falcoz_, Mar 11 2019
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