A277446 Longest partition of the binary digits of n read from left to right into contiguous blocks so that the value of a block divides the value of its successor and with no leading zeros in the blocks.

1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 2, 2, 3, 4, 1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 3, 2, 3, 3, 4, 5, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 2, 2, 1, 2, 2, 2, 2, 3, 2, 3, 2, 3, 3, 4, 3, 4, 4, 5, 6, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 3, 1, 3, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 4, 2

Offset

1,3

Links

Table of n, a(n) for n=1..107.

Marko Riedel, Maple code to compute sequence.

Example

We have 58 = (1,1,1,0,1,0)_2 and (1)_2|(1)_2|(1,0)_2|(1,0)_2 yielding the value four.
We have 676 = (1,0,1,0,1,0,0,1,0,0)_2 and (1,0)_2|(1,0)_2|(1,0,0)_2|(1,0,0)_2 yielding the value four.

Prog

(PARI) okp(p, b) = {vb = vector(#p); vv = vector(#p); j = 1; for (k=1, #p, vb[k] = vector(p[k], m, b[j+m-1]); if ((vb[k])[1] == 0, return (0)); vv[k] = subst(Pol(vb[k]), x, 2); if ((k >1) && (vv[k] % vv[k-1]), return (0)); j += p[k]; ); 1; }
a(n) = {b = binary(n); nb = 0; forpart(p=#b, if (okp(p, b), nb = max(nb, #p)); ); nb; } \\ Michel Marcus, Oct 18 2016

Crossrefs

Cf. A277447, A277448.

Sequence in context: A265743 A082850 A290695 * A334029 A334297 A333765

Adjacent sequences: A277443 A277444 A277445 * A277447 A277448 A277449

Keyword

nonn,base

Author

Marko Riedel, Oct 15 2016

Status

approved