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.

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

Author

Eric Angelini and Carole Dubois, May 16 2019

Keywords

• base
• nonn

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.
		

Links

• Carole Dubois, Table of n, a(n) for n = 1..5001
• Carole Dubois, Digit-count for this sequence and two others visible in the Xref section

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.