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 A306808 #8 Mar 12 2019 22:31:10 %S A306808 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 A306808 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 A306808 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 A306808 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 A306808 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 A306808 Jean-Marc Falcoz, <a href="/A306808/b306808.txt">Table of n, a(n) for n = 1..10002</a> %e A306808 S starts with a(1) = 1 and a(2) = 9 %e A306808 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 A306808 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 A306808 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 A306808 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 A306808 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 A306808 Etc. %Y A306808 Cf. A306803 (which is obtained by replacing palindrome by prime in the definition). %K A306808 base,nonn,look %O A306808 1,2 %A A306808 _Eric Angelini_ and _Jean-Marc Falcoz_, Mar 11 2019