A281114 Parity of the n-th squarefree triangular number.

1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1

Offset

1

Comments

The sequence giving the parity of all triangular numbers is periodic with period 4 after the initial 0, A000217(n) mod 2 = A021913(n+1).

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = A061304(n) mod 2.

Example

The eighth squarefree triangular number is 66, which is even, so a(8) = 0.

Maple

map(t -> `if`(t-1 mod 4 <= 1, 1, 0), select(t -> numtheory:-issqrfree(t*(t+1)/2), [$1..1000])); # Robert Israel, Oct 09 2017

Mathematica

Boole@ OddQ@ # & /@ Select[PolygonalNumber@ Range@ 210, SquareFreeQ] (* Michael De Vlieger, Oct 06 2017 *)

Crossrefs

Cf. A000217, A061304, A021913.

Sequence in context: A323511 A284391 A127015 * A286749 A359374 A188192

Adjacent sequences: A281111 A281112 A281113 * A281115 A281116 A281117

Keyword

nonn

Author

Rick L. Shepherd, Jan 14 2017

Status

approved