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

1,3

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.

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)

Example

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

Prog

(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)

Crossrefs

Cf. A248034.

Sequence in context: A359031 A248034 A358967 * A356348 A336514 A358851

Adjacent sequences: A322179 A322180 A322181 * A322183 A322184 A322185

Keyword

nonn,base

Author

Rémy Sigrist, Nov 30 2018

Status

approved