This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A090049 #17 Jul 30 2025 01:00:18
%S A090049 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 A090049 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 A090049 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 A090049 Length of longest contiguous block of 0's in binary expansion of n^3.
%H A090049 Robert Israel, <a href="/A090049/b090049.txt">Table of n, a(n) for n = 0..10000</a>
%F A090049 a(n) = A087117(A000578(n)).
%F A090049 a(n) <= 3*A070939(n) - 3 for n > 0. - _Charles R Greathouse IV_, Mar 10 2020
%F A090049 a(n) >= 3*A007814(n). Conjecture: if n < 2^k then a(n) < 3*k. - _Robert Israel_, Mar 10 2020
%p A090049 f:= proc(n) local R;
%p A090049 R:= convert(2*n^3+1,base,2);
%p A090049 R:= select(t -> R[t]=1, [$1..nops(R)]);
%p A090049 max(R[2..-1]-R[1..-2])-1
%p A090049 end proc:
%p A090049 f(0):= 1:
%p A090049 map(f, [$0..100]); # _Robert Israel_, Mar 10 2020
%t A090049 a[n_] := Module[{d = IntegerDigits[n^3, 2]}, If[! MemberQ[d, 0], 0, Max[Length /@ Split[d][[2 ;; -1 ;; 2]]]]]; a[0] = 1; Array[a, 102, 0] (* _Amiram Eldar_, Jul 29 2025 *)
%o A090049 (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 A090049 Cf. A000578, A007814, A023416, A070939, A087117, A090003, A090047, A090048.
%K A090049 nonn,base,easy
%O A090049 0,3
%A A090049 _Reinhard Zumkeller_, Nov 20 2003