A090049 Length of longest contiguous block of 0's in binary expansion of n^3.

1, 0, 3, 1, 6, 1, 3, 1, 9, 2, 3, 2, 6, 3, 3, 2, 12, 3, 3, 2, 6, 4, 3, 4, 9, 4, 3, 3, 6, 3, 3, 3, 15, 4, 3, 2, 6, 3, 3, 2, 9, 4, 4, 2, 6, 3, 4, 3, 12, 3, 4, 6, 6, 3, 3, 3, 9, 2, 3, 4, 6, 2, 3, 4, 18, 5, 4, 2, 6, 6, 3, 4, 9, 2, 3, 2, 6, 1, 3, 4, 12, 6, 4, 3, 6, 2, 3, 5, 9, 5, 3, 3, 6, 6, 3, 3, 15, 4, 3

Offset

0,3

Comments

a(n) >= 3*A007814(n). Conjecture: if n < 2^k then a(n) < 3*k. - Robert Israel, Mar 10 2020

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Formula

a(n) = A087117(A000578(n)).

a(n) <= 3*A070939(n) - 3 for n > 0. - Charles R Greathouse IV, Mar 10 2020

Maple

f:= proc(n) local R;
  R:= convert(2*n^3+1, base, 2);
  R:= select(t -> R[t]=1, [$1..nops(R)]);
  max(R[2..-1]-R[1..-2])-1
end proc:
f(0):= 1:
map(f, [$0..100]); # Robert Israel, Mar 10 2020

Prog

(PARI) a(n)=my(r, k, t=n^3); for(i=0, exponent(t), if(bittest(t, i), k=0, k++>r, r=k)); if(n, r, 1) \\ Charles R Greathouse IV, Mar 10 2020

Crossrefs

Cf. A000578, A007814, A023416, A087117, A090047, A090048, A090003.

Sequence in context: A010287 A130270 A225599 * A115364 A016476 A293436

Adjacent sequences: A090046 A090047 A090048 * A090050 A090051 A090052

Keyword

nonn,base,easy

Author

Reinhard Zumkeller, Nov 20 2003

Status

approved