A336037 a(n+1) is the number of times the binary representation of a(n) is the concatenation of that of one or more consecutive terms in this sequence so far with a(1) = 1.

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

Offset: 1

Author

Rémy Sigrist, Jul 07 2020

Keywords

• nonn
• base

Comments

This sequence has similarities with A331614 and A332518; here we concatenate consecutive terms, there we add and multiply them, respectively.

This sequence is unbounded.

Examples

			The first terms, alongside their binary representation and the corresponding concatenations, are:
  n   a(n)  bin(a(n))  Concatenations
  --  ----  ---------  --------------
   1     1          1  a(1)
   2     1          1  a(1), a(2)
   3     2         10  a(3)
   4     1          1  a(1), a(2), a(4)
   5     3         11  a(1)|a(2), a(5)
   6     2         10  a(3), a(6)
   7     2         10  a(3), a(6), a(7)
   8     3         11  a(1)|a(2), a(5), a(8)
   9     3         11  a(1)|a(2), a(5), a(8), a(9)
  10     4        100  a(10)
		

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 A336037

Crossrefs

Cf. A331614, A332518.

Programs

PARI

See Links section.