cp's OEIS Frontend

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.

%I A333441 #8 Mar 07 2021 05:53:30
%S A333441 0,3,9,12,15,33,36,39,45,48,51,54,57,60,63,129,132,135,141,144,147,
%T A333441 150,153,156,159,165,177,180,183,189,192,195,198,201,204,207,210,216,
%U A333441 219,222,225,228,231,237,240,243,246,249,252,255,513,516,519,525,528,531
%N 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.
%C A333441 The term 0 is included by convention (we consider here that it has no digit).
%C A333441 This sequence is a binary variant of A333440.
%C A333441 Every term belong to A059012.
%C A333441 This sequence has connections with A014486; in both sequences digits are balanced in some way.
%H A333441 Rémy Sigrist, <a href="/A333441/b333441.txt">Table of n, a(n) for n = 1..8789</a> (terms < 2^16)
%e A333441 The first terms, alongside their binary representation with a possible pairing, are:
%e A333441   n   a(n)  bin(a(n))
%e A333441   --  ----  ------------
%e A333441    1     0  0
%e A333441    2     3  (11)
%e A333441    3     9  (1(00)1)
%e A333441    4    12  (11)(00)
%e A333441    5    15  (11)(11)
%e A333441    6    33  (1(00)(00)1)
%e A333441    7    36  (1(00)1)(00)
%e A333441    8    39  (1(00)1)(11)
%e A333441    9    45  (1(0(11)0)1)
%e A333441   10    48  (11)(00)(00)
%e A333441   11    51  (11)(00)(11)
%e A333441   12    54  (11)(0(11)0)
%e A333441   13    57  (11)(1(00)1)
%e A333441   14    60  (11)(11)(00)
%e A333441   15    63  (11)(11)(11)
%o A333441 (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 }
%Y A333441 Cf. A014486, A059012, A333440.
%K A333441 nonn,base
%O A333441 1,2
%A A333441 _Rémy Sigrist_, Mar 21 2020