A309342 a(1) = 0, and for n >= 1, a(n+1) is the number of times the binary representation of a(n) appears in the concatenation of the binary representations of a(1), ..., a(n-1).

0, 0, 1, 0, 2, 1, 2, 2, 3, 1, 7, 1, 11, 2, 5, 5, 7, 7, 9, 0, 12, 1, 30, 2, 12, 2, 14, 4, 3, 26, 4, 4, 5, 15, 13, 7, 24, 0, 34, 0, 39, 2, 27, 3, 45, 3, 49, 0, 49, 1, 89, 2, 36, 2, 39, 3, 60, 3, 66, 1, 112, 2, 45, 4, 19, 6, 26, 6, 28, 6, 30, 12, 12, 13, 20, 4

Offset

1,5

Comments

This sequence is a binary variant of A276457.

This sequence is necessarily unbounded.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Logarithmic scatterplot of the first 250000 terms

Rémy Sigrist, Perl program for A309342

Example

The first terms, alongside the binary representations of a(n) and of a(1), ..., a(n-1) with marks in front of occurrences of a(n), are:
  n   a(n)  bin(a(n))  bin(a(1)...a(n-1))
  --  ----  ---------  --------------------
   1     0          0
   2     0          0                    [0
   3     1          1                    00
   4     0          0                 [0[01
   5     2         10                 00[10
   6     1          1              00[10[10
   7     2         10             00[10[101
   8     2         10          00[10[101[10
   9     3         11          001010[11010
  10     1          1  00[10[10[1[10[10[1[1
  11     7        111       00101011010[111

Prog

(Perl) See Links section.

Crossrefs

Cf. A276457.

Sequence in context: A328220 A134192 A358344 * A380117 A284044 A126305

Adjacent sequences: A309339 A309340 A309341 * A309343 A309344 A309345

Keyword

nonn,base

Author

Rémy Sigrist, Jul 24 2019

Status

approved