A336514 a(1) = 1, and for any n > 0, a(n+1) is the number of k in the range 1..n such that the decimal representation of a(k) appears as a substring in the decimal representation of a(n).

1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 8, 1, 9, 1, 10, 11, 11, 12, 12, 13, 12, 14, 12, 15, 12, 16, 12, 17, 12, 18, 12, 19, 12, 20, 2, 2, 3, 2, 4, 2, 5, 2, 6, 2, 7, 2, 8, 2, 9, 2, 10, 12, 30, 3, 3, 4, 3, 5, 3, 6, 3, 7, 3, 8, 3, 9, 3, 10, 13, 22, 11, 13, 23

Offset: 1

Author

Rémy Sigrist, Jul 24 2020

Keywords

• nonn
• look
• base

Comments

This sequence is unbounded.

Examples

			The first terms, alongside the corresponding k's, are:
  n   a(n)  k's
  --  ----  -----------
   1     1  N/A
   2     1  {1}
   3     2  {1, 2}
   4     1  {3}
   5     3  {1, 2, 4}
   6     1  {5}
   7     4  {1, 2, 4, 6}
   8     1  {7}
   9     5  {1, 2, 4, 6, 8}
  10     1  {9}
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Density plot of the first 100000000 terms
• Rémy Sigrist, PARI program for A336514

Crossrefs

Cf. A336515 (binary variant).

Programs

PARI

See Links section.