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 A308386 #23 May 26 2019 01:40:44 %S A308386 5,14,84,10,1,20,21,22,17,4,4,27,11,2,98,99,9,34,1,6,7,8,9,4,12,6,12, %T A308386 4,9,36,4,12,9,18,9,36,4,12,9,18,6,12,4,9,36,4,12,9,18,9,30,6 %N A308386 A self-describing sequence when translated into English: duplicate the n-th letter of the sequence at position a(n). When all the duplications are done, the result is the sequence itself. %C A308386 The author is almost sure that this sequence, unfortunately, is not the lexicographically earliest of its kind. %H A308386 Eric Angelini, <a href="https://cinquantesignes.blogspot.com/2019/03/two-self-describing-sequences-for.html">Two self-describing sequences</a>. %e A308386 The sequence starts 5,14,84,10,1,... Translated into English, omitting hyphens: %e A308386 FIVE FOURTEEN EIGHTYFOUR TEN ONE ... %e A308386 We start reading the English words from the left to the right, letter by letter; %e A308386 the first letter is F; we then duplicate this F to the 5th position, as a(1) = 5 (this new F is visible in FOURTEEN); %e A308386 We now read the 2nd letter (I) and duplicate it at position 14, as a(2) = 14 (this new I is visible in EIGHTYFOUR); %e A308386 We now read the 3rd letter (V) and duplicate it at position 84, as a(3) = 84 (this new V is visible in ELEVEN); %e A308386 We now read the 4th letter (E) and duplicate it at position 10, as a(4) = 10 (this new E is visible in FOURTEEN, first E); %e A308386 We now read the 5th letter (F) and duplicate it at position 1, as a(5) = 1 (this "new" F is visible in FIVE, first word); etc. %e A308386 The duplication rule is: a numerical term a(n) cannot command the duplication of one of its own letters, when translated in English -- otherwise, the lexicographically first sequence would simply be 1, 2, 3, 4, 5, ... ONE, TWO, THREE, FOUR, FIVE, ... where every letter is "duplicated" on itself. We see with this counterexample that the sequence cannot start with a(1) = 1 (ONE) as the letter O would be duplicated on itself; neither can it start with a(1) = 2 (TWO) as the 2nd letter of the sequence is not a T; neither with 3 (THREE) as the 3rd letter of the sequence is not a T; neither with 4 (FOUR) as the 4th letter of the sequence is not a F; but 5 is ok: the 5th letter of the sequence is indeed F, and this F doesn't belong to the English translation of a(1). %Y A308386 Cf. A308387 (illustrates the same idea, but with digits instead of letters). %K A308386 base,nonn,word,more %O A308386 1,1 %A A308386 _Eric Angelini_, May 23 2019