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

0,8

Links

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

Formula

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

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 *)

Crossrefs

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

Sequence in context: A232504 A292201 A343070 * A064285 A006694 A210481

Adjacent sequences: A090045 A090046 A090047 * A090049 A090050 A090051

Keyword

nonn,base

Author

Reinhard Zumkeller, Nov 20 2003

Status

approved