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.

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A308232 Start the sequence with a(1) = 1 and read the digits one by one from there. The sequence is always extended with the concatenation kd, d being the digit that was read and k the number of d's present so far in the sequence.

Original entry on oeis.org

1, 11, 21, 31, 12, 41, 13, 51, 61, 22, 14, 71, 81, 23, 15, 91, 16, 101, 32, 42, 111, 24, 17, 121, 18, 131, 52, 33, 141, 25, 19, 151, 161, 26, 171, 10, 181, 43, 62, 34, 72, 191, 201, 211, 82, 44, 221, 27, 231, 92, 241, 251, 28, 261, 53, 271, 35, 102, 63, 73, 281, 54, 291, 112, 45, 301, 29, 311, 55, 321, 331, 36, 341, 122, 46, 351
Offset: 1

Views

Author

Eric Angelini and Carole Dubois, May 16 2019

Keywords

Comments

All integers > 0 will appear exactly once, except 2, 3, 4, 5, 6, 7, 8 and 9 which will never appear.

Examples

			The sequence starts with a(1) = 1.
We read this 1, see that there is only one digit 1 so far in the sequence, thus k = 1; we have then [kd] = 11 and this 11 becomes a(2);
We read now the first digit of a(2) = 11, which is 1; as this 1 is the 2nd occurrence of 1 so far in the sequence, we have k = 2 and [kd] = 21; this 21 becomes a(3);
We read now the second digit of a(2) = 11, which is 1; as this 1 is the 3rd occurrence of 1 so far in the sequence, we have k = 3 and [kd] = 31; this 31 becomes a(4);
We read now the first digit of a(3) = 21, which is 2; as this 2 is the 1st occurrence of 2 so far in the sequence, we have k = 1 and [kd] = 12; this 12 becomes a(5);
We read now the second digit of a(3) = 21, which is 1; as this 1 is the 4th occurrence of 1 so far in the sequence, we have k = 4 and [kd] = 41; this 41 becomes a(6); etc.
		

Crossrefs

Cf. A325721 and A325722 where the same idea is developed (addition and multiplication instead of concatenation).

A325721 Start the sequence with a(1) = 1 and read the digits one by one from there. The sequence is always extended with the sum d + k, d being the digit read and k the number of d digits present so far in the sequence.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 3, 1, 5, 4, 7, 6, 9, 8, 11, 10, 5, 6, 7, 2, 8, 9, 10, 4, 11, 12, 8, 3, 7, 9, 10, 11, 5, 12, 6, 11, 13, 12, 4, 13, 14, 9, 15, 6, 10, 16, 17, 18, 7, 19, 7, 8, 20, 8, 21, 9, 14, 22, 10, 11, 23, 5, 24, 12, 25, 12, 26, 13, 13, 27, 15, 14, 14, 8, 6, 15, 9, 28, 16, 29, 10, 10, 11, 30, 7, 31, 32, 12, 9, 11, 13, 11
Offset: 1

Views

Author

Eric Angelini and Carole Dubois, May 16 2019

Keywords

Examples

			The sequence starts with a(1) = 1.
We read this 1, see that there is only one digit 1 so far in the sequence, thus k = 1; we have then d + k = (1 + 1) = 2 and this 2 becomes a(2);
We read this 2, see that there is only one digit 2 so far in the sequence, thus k = 1; we have then d + k = (2 + 1) = 3 and this 3 becomes a(3);
We read this 3, see that there is only one digit 3 so far in the sequence, thus k = 1; we have then d + k = (3 + 1) = 4 and this 4 becomes a(4);
...
We now read the first digit of a(10) = 10, see that this 1 is the 2nd digit 1 so far in the sequence, thus k = 2; we have then d + k = (1 + 2) = 3 and this 3 becomes a(11);
We now read the second digit of a(10) = 10, see that this 0 is the 1st digit 0 so far in the sequence, thus k = 1; we have then d + k = 1 and this 1 becomes a(12);
We now read the single digit of a(11) = 3; we see that this 3 is the 2nd digit 3 so far in the sequence, thus k = 2; we have then d + k = 5 and this 5 becomes a(13); etc.
		

Crossrefs

Cf. A325722 where the same idea is developed, but with d*k instead of d+k. See also A308232 for the concatenation kd.
Cf. A322182.
Showing 1-2 of 2 results.