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

1,3

Comments

This sequence is unbounded.

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

Example

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}

Prog

(PARI) See Links section.

Crossrefs

Cf. A336515 (binary variant).

Sequence in context: A358967 A322182 A356348 * A358851 A249009 A162520

Adjacent sequences: A336511 A336512 A336513 * A336515 A336516 A336517

Keyword

nonn,look,base

Author

Rémy Sigrist, Jul 24 2020

Status

approved