A387219 Product of the first n terms of the paperfolding sequence A034947, or the Kronecker symbol (-1|n!).

1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1

Offset

1

Comments

A 2-automatic sequence.

Links

Table of n, a(n) for n=1..73.

Formula

a(n) = (-1)^A255070(n). - Kevin Ryde, Dec 31 2025

Example

For n=4, the first 4 terms of A034947 are 1,1,-1,1 and their product is a(4) = -1.

Mathematica

FoldList[Times, Table[KroneckerSymbol[-1, n], {n, 1, 100}]] (* Amiram Eldar, Dec 22 2025 *)

Prog

(PARI) a(n) = if(bittest(n, 1) == bittest(hammingweight(bitxor(n, n>>1)), 1), 1, -1); \\ Kevin Ryde, Dec 31 2025

Crossrefs

Cf. A034947, A255070.

Sequence in context: A262725 A070748 A154990 * A209615 A242179 A319117

Adjacent sequences: A387216 A387217 A387218 * A387220 A387221 A387222

Keyword

sign,easy

Author

Jeffrey Shallit, Dec 22 2025

Status

approved