cp's OEIS Frontend

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.

Showing 1-3 of 3 results.

A347691 a(n) = index of n in A308387, or -1 if n does not appear in A308387.

Original entry on oeis.org

20, 1, 11, 10, 8, 3, 38, 5, 17, 4, 6, 19, 9, 16, 24, 14, 21, 27, 12, 2, 25, 36, 28, 15, 32, 43, 18, 23, 74, 33, 37, 39, 42, 29, 44, 22, 31, 46, 45, 56, 47, 52, 26, 48, 61, 60, 41, 49, 53, 73, 59, 13, 57, 91, 64, 40, 66, 62, 51, 7, 30, 58, 101, 55, 70, 69, 86, 34, 75, 65, 80, 78, 50
Offset: 1

Views

Author

N. J. A. Sloane, Sep 26 2021

Keywords

Examples

			A308387(20) = 1, so a(1) = 20.

Links

Crossrefs

Cf. A308387.

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.

Original entry on oeis.org

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
Offset: 1

Views

Author

Eric Angelini, May 23 2019

Keywords

Comments

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

Examples

			The sequence starts 5,14,84,10,1,... Translated into English, omitting hyphens:
FIVE FOURTEEN EIGHTYFOUR TEN ONE ...
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).

Links

Crossrefs

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

A342164 A self-describing sequence: start with 0, then for each digit in each successive term, starting from the first term, append to the sequence its most recent position in the string formed by the concatenation of all previous terms.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 17, 19, 16, 23, 18, 27, 30, 27, 22, 27, 24, 39, 41, 44, 28, 47, 50, 41, 52, 56, 50, 56, 56, 56, 50, 56, 53, 72, 42, 75, 54, 80, 80, 76, 83, 80, 85, 92, 90, 80, 54, 99, 94, 99, 86, 99, 98, 99, 108, 99, 108, 99, 108, 99, 126, 99
Offset: 0

Views

Author

Scott R. Shannon, Mar 03 2021

Keywords

Comments

After the leading zero taking the a(n)-th digit of the sequence returns the digits of the sequence.

Examples

			The second term is 1 as the 0 in the first term appears as the first digit in the sequence. Likewise the third term is 2 as the 1 in the second term is the second digit of the sequence, and so on to the eleventh term.
As the eleventh term is 10 and has two digits, the twelfth and thirteenth terms give the most recent position of a 1 and 0 in the sequence, and they appear at the eleventh and twelfth position.
As the twelfth term is 11, the fourteenth and fifteenth terms give the most recent position of the two 1's. The last 1 appears at the fifteenth position, and after appending 15, which contains a 1, the most recent 1 now appears at the seventeenth position.

Crossrefs

Cf. A125132, A264646, A114308, A263563, A308387
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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