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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). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 16 21:55 EDT 2021. Contains 345080 sequences. (Running on oeis4.)