A336515 a(1) = 1, and for any n > 0, a(n+1) is the number of k in the range 1..n such that the binary representation of a(k) appears as a substring in the binary representation of a(n).

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

Offset: 1

Author

Rémy Sigrist, Jul 24 2020

Keywords

• nonn
• look
• base

Comments

This sequence is unbounded.

Examples

			The first terms, alongside their binary representation and the corresponding k's, are:
  n   a(n)  bin(a(n))  k's
  --  ----  ---------  -------------
   1     1          1  N/A
   2     1          1  {1}
   3     2         10  {1, 2}
   4     3         11  {1, 2, 3}
   5     3         11  {1, 2, 4}
   6     4        100  {1, 2, 4, 5}
   7     4        100  {1, 2, 3, 6}
   8     5        101  {1, 2, 3, 6, 7}
   9     4        100  {1, 2, 3, 8}
  10     6        110  {1, 2, 3, 6, 7, 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 A336515

Crossrefs

Cf. A336514 (decimal variant).

Programs

PARI

See Links section.