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

1,3

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 A336515

Example

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}

Prog

(PARI) See Links section.

Crossrefs

Cf. A336514 (decimal variant).

Sequence in context: A300118 A256544 A321211 * A130500 A072073 A320757

Adjacent sequences: A336512 A336513 A336514 * A336516 A336517 A336518

Keyword

nonn,look,base

Author

Rémy Sigrist, Jul 24 2020

Status

approved