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

1,2

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.

Links

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

Example

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)

Prog

(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 }

Crossrefs

Cf. A014486, A059012, A333440.

Sequence in context: A136290 A244147 A103531 * A108860 A006499 A310320

Adjacent sequences: A333438 A333439 A333440 * A333442 A333443 A333444

Keyword

nonn,base

Author

Rémy Sigrist, Mar 21 2020

Status

approved