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

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, 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, 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

Offset: 0

Author

Reinhard Zumkeller, Nov 20 2003

Keywords

• nonn
• base

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000217, A023416, A087117, A090002, A090047, A090049.

Programs

Mathematica

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 *)

Formula

a(n) = A087117(A000217(n)).