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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.
4
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, 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
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Nov 30 2018
STATUS
approved