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A243112 a(n) is the smallest number that requires at least n adjacent bit swaps in order to pack all the ones to the right.

%I A243112 #26 Oct 04 2024 16:12:48
%S A243112 0,2,4,8,12,20,24,40,48,56,88,104,112,176,208,224,240,368,432,464,480,
%T A243112 736,864,928,960,992,1504,1760,1888,1952,1984,3008,3520,3776,3904,
%U A243112 3968,4032,6080,7104,7616,7872,8000,8064,12160,14208,15232,15744,16000,16128
%N A243112 a(n) is the smallest number that requires at least n adjacent bit swaps in order to pack all the ones to the right.
%C A243112 a(n) = i if and only if A055941(i) == n and A055941(j) < n for all j < i.
%C A243112 Indices where records of A055941 occur.
%H A243112 Philippe Beaudoin, <a href="/A243112/b243112.txt">Table of n, a(n) for n = 0..132</a>
%o A243112 (PARI) a055941(n) = {my(b=binary(n)); nb = 0; for (i=1, #b-1, if (b[i], nb += sum(j=i+1, #b, !b[j])); ); nb; }
%o A243112 lista(nn) = {vmax = 0; print1(vmax, ", "); for (n=1, nn, vnew = a055941(n); if (vnew > vmax, vmax = vnew; print1(n, ", ");););} \\ _Michel Marcus_, Aug 29 2014
%o A243112 (Python)
%o A243112 A243112, a = [0], 0
%o A243112 for n in range(1, 2**30):
%o A243112     s = bin(n)[2:]
%o A243112     b = sum(s[i:].count('0') for i, d in enumerate(s, start=1) if d == '1')
%o A243112     if b > a:
%o A243112         A243112.append(n)
%o A243112         a = b # _Chai Wah Wu_, Sep 07 2014
%Y A243112 Cf. A055941.
%K A243112 nonn,base
%O A243112 0,2
%A A243112 _Philippe Beaudoin_, Aug 20 2014