A117964 a(n) = A117963(n) mod 2.

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

Offset: 0

Author

Paul Barry, Apr 05 2006

Keywords

• easy
• nonn

Comments

a(3n+2) = 0, a(3n) = a(3n+1). a(3n) may be equal to A088917(n).

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16384
• Index entries for characteristic functions

Crossrefs

Cf. A000035, A005836, A117963, A081601, A088917.

Formula

a(n)=sum{k=0..floor(n/2), L(C(n-k,k)/3)} mod 2 where L(j/p) is the Legendre symbol of j and p.

a(2*A081601(n)) = a(1+2*A081601(n)) = 1. [Conjectured, also these two formulas together seem to give the positions of all 1's] - Antti Karttunen, Jan 01 2023