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A090048 Length of longest contiguous block of 0's in binary expansion of n-th triangular number.

%I A090048 #8 Jul 30 2025 01:00:32
%S A090048 1,0,0,1,1,0,1,2,2,1,1,4,2,1,2,3,3,2,1,1,2,2,1,3,2,3,1,1,2,2,3,4,4,3,
%T A090048 2,2,2,1,2,4,2,1,4,2,1,6,4,3,3,2,2,2,3,2,2,6,3,2,1,1,2,3,4,5,5,4,3,3,
%U A090048 2,2,2,2,3,3,1,3,1,1,6,3,3,2,2,2,2,3,2,2,2,2,0,5,4,3,3,4,4,3,2,2,2,5
%N A090048 Length of longest contiguous block of 0's in binary expansion of n-th triangular number.
%H A090048 Amiram Eldar, <a href="/A090048/b090048.txt">Table of n, a(n) for n = 0..10000</a>
%F A090048 a(n) = A087117(A000217(n)).
%t A090048 a[n_] := Module[{d = IntegerDigits[n*(n + 1)/2, 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 *)
%Y A090048 Cf. A000217, A023416, A087117, A090002, A090047, A090049.
%K A090048 nonn,base
%O A090048 0,8
%A A090048 _Reinhard Zumkeller_, Nov 20 2003