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.

0, 2, 4, 8, 12, 20, 24, 40, 48, 56, 88, 104, 112, 176, 208, 224, 240, 368, 432, 464, 480, 736, 864, 928, 960, 992, 1504, 1760, 1888, 1952, 1984, 3008, 3520, 3776, 3904, 3968, 4032, 6080, 7104, 7616, 7872, 8000, 8064, 12160, 14208, 15232, 15744, 16000, 16128

Offset

0,2

Comments

a(n) = i if and only if A055941(i) == n and A055941(j) < n for all j < i.

Indices where records of A055941 occur.

Links

Philippe Beaudoin, Table of n, a(n) for n = 0..132

Prog

(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; }
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
(Python)
A243112, a = [0], 0
for n in range(1, 2**30):
    s = bin(n)[2:]
    b = sum(s[i:].count('0') for i, d in enumerate(s, start=1) if d == '1')
    if b > a:
        A243112.append(n)
        a = b # Chai Wah Wu, Sep 07 2014

Crossrefs

Cf. A055941.

Sequence in context: A127405 A344932 A136034 * A230127 A059793 A118029

Adjacent sequences: A243109 A243110 A243111 * A243113 A243114 A243115

Keyword

nonn,base

Author

Philippe Beaudoin, Aug 20 2014

Status

approved