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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. 1
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, 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 (list; graph; refs; listen; history; text; internal format)



The author is almost sure that this sequence, unfortunately, is not the lexicographically earliest of its kind.


Table of n, a(n) for n=1..52.

Eric Angelini, Two self-describing sequences.


The sequence starts 5,14,84,10,1,... Translated into English, omitting hyphens:


We start reading the English words from the left to the right, letter by letter;

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);

We now read the 2nd letter (I) and duplicate it at position 14, as a(2) = 14 (this new I is visible in EIGHTYFOUR);

We now read the 3rd letter (V) and duplicate it at position 84, as a(3) = 84 (this new V is visible in ELEVEN);

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);

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.

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).


Cf. A308387 (illustrates the same idea, but with digits instead of letters).

Sequence in context: A320800 A321315 A203225 * A198039 A198091 A197797

Adjacent sequences:  A308383 A308384 A308385 * A308387 A308388 A308389




Eric Angelini, May 23 2019



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Last modified September 21 01:46 EDT 2021. Contains 347596 sequences. (Running on oeis4.)