A090049 - OEIS

%I #12 Mar 10 2020 13:05:17

%S 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,

%T 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,

%U 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

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

%C a(n) >= 3*A007814(n). Conjecture: if n < 2^k then a(n) < 3*k. - _Robert Israel_, Mar 10 2020

%H Robert Israel, <a href="/A090049/b090049.txt">Table of n, a(n) for n = 0..10000</a>

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

%F a(n) <= 3*A070939(n) - 3 for n > 0. - _Charles R Greathouse IV_, Mar 10 2020

%p f:= proc(n) local R;

%p   R:= convert(2*n^3+1,base,2);

%p   R:= select(t -> R[t]=1, [$1..nops(R)]);

%p   max(R[2..-1]-R[1..-2])-1

%p end proc:

%p f(0):= 1:

%p map(f, [$0..100]); # _Robert Israel_, Mar 10 2020

%o (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

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

%K nonn,base,easy

%O 0,3

%A _Reinhard Zumkeller_, Nov 20 2003