A322182 a(1) = 1, and for any n > 0, a(n+1) is the number of occurrences of the n-th digit of the sequence among the first n digits of the sequence.

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

Offset: 1

Author

Rémy Sigrist, Nov 30 2018

Keywords

• nonn
• base

Comments

In other words, if we take the ordinal transform of the digits of the sequence and prepend the number 1, then we obtain the sequence again.

The number 1 appears 11 times.

Any number > 1 appears 10 times.

The sequence contains arbitrarily large runs of consecutive numbers.

Examples

			The first terms of the sequence, alongside the (n-1)-th digit of the sequence, are:
  n    a(n)  (n-1)-th digit
  ---  ----  --------------
    1     1             N/A
    2     1               1
    3     2               1
    4     1               2
    5     3               1
    6     1               3
    7     4               1
    8     1               4
    9     5               1
   10     1               5
   11     6               1
   12     1               6
   13     7               1
   14     1               7
   15     8               1
   16     1               8
   17     9               1
   18     1               9
   19    10               1
   20    11               1
   21     1               0
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Colored scatterplot of (n, a(n)) for n = 1..1000000 (where the color is function of the n-th digit of the sequence)

Crossrefs

Cf. A248034.

Programs

PARI

a = [1]; ord = vector(base = 10); for (k=1, 59, a = concat(a, apply(d -> ord[1+d]++, digits(a[k], #ord)))); print (a)