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

Author

Philippe Beaudoin, Aug 20 2014

Keywords

• nonn
• base

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

Crossrefs

Cf. A055941.

Programs

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