A333441 Numbers where each binary digit can be paired with a digit of the same value at another position so that two pairs can be nested but cannot otherwise overlap.

0, 3, 9, 12, 15, 33, 36, 39, 45, 48, 51, 54, 57, 60, 63, 129, 132, 135, 141, 144, 147, 150, 153, 156, 159, 165, 177, 180, 183, 189, 192, 195, 198, 201, 204, 207, 210, 216, 219, 222, 225, 228, 231, 237, 240, 243, 246, 249, 252, 255, 513, 516, 519, 525, 528, 531

Offset: 1

Author

Rémy Sigrist, Mar 21 2020

Keywords

• nonn
• base

Comments

The term 0 is included by convention (we consider here that it has no digit).

This sequence is a binary variant of A333440.

Every term belong to A059012.

This sequence has connections with A014486; in both sequences digits are balanced in some way.

Examples

			The first terms, alongside their binary representation with a possible pairing, are:
  n   a(n)  bin(a(n))
  --  ----  ------------
   1     0  0
   2     3  (11)
   3     9  (1(00)1)
   4    12  (11)(00)
   5    15  (11)(11)
   6    33  (1(00)(00)1)
   7    36  (1(00)1)(00)
   8    39  (1(00)1)(11)
   9    45  (1(0(11)0)1)
  10    48  (11)(00)(00)
  11    51  (11)(00)(11)
  12    54  (11)(0(11)0)
  13    57  (11)(1(00)1)
  14    60  (11)(11)(00)
  15    63  (11)(11)(11)
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..8789 (terms < 2^16)

Crossrefs

Cf. A014486, A059012, A333440.

Programs

PARI

is(n, base=2) = { my (u=0, s=0); while (n, my (d=n%base); if (u && s%base==d, u--; s\=base, u++; s=s*base+d); n\=base); u==0 }