[seqfan] The digital root of a(n) is the a(n)th digit of the sequence

[Eric Angelini]

Hello SeqFans,

T=1,2,3,4,5,6,7,8,9,10,14,50,13,20,22,40,26,80,30,32,51,36,90,45,44,89,48,305,60,55,100,61,67,64,101,400,70,74,102,79,780,84,300,91,891,93,95,97,99,123,106,700,109,115,701,118,126,129,133,127,...

The digital root of a(n) is the a(n)th digit of T.

Example:
- 10 is in the sequence because the 10th digit of T is 1 (and 1 is the digital root of 10)
- 14 is in the sequence because the 14th digit of T is 5 (and 5 is the digital root of 14)
- 50 is in the sequence because the 50th digit of T is 5 (and 5 is the digital root of 14)
- 13 is in the sequence because the 13th digit of T is 4 (and 4 is the digital root of 14)
...
T is infinite as it is always possible to "postpone" the problems
and find an unused integer to extend T without contradictions.

For instance, in extending T from now, we must keep in mind that:
- the 300th digit of T is 3
- the 305th digit of T is 8
- the 400th digit of T is 4
- the 700th digit of T is 7
- the 701st digit of T is 8
- the 702nd digit of T is 9
- the 780th digit of T is 6
- the 891st digit of T is 9

This will cause no problem -- just long integers!
[T is of course not a permutation of the integers > 0 as the zero 
 of 10, for instance, cannot be a digital root]

Best,
É.