A338241 - OEIS

%I #11 Oct 18 2020 22:32:35

%S 0,1,-1,3,-2,2,-3,4,-4,9,-8,8,-6,7,-7,6,-5,5,-9,10,-10,12,-11,11,-12,

%T 13,-13,27,-26,26,-24,25,-25,24,-23,23,-18,19,-19,21,-20,20,-21,22,

%U -22,18,-17,17,-15,16,-16,15,-14,14,-27,28,-28,30,-29,29,-30,31

%N For any m >= 0, a(3*m) = 3*a(m), a(3*m+1) = 1-3*a(m), a(3*m+2) = 3*a(m)-1.

%C This sequence is a variant of A117966.

%C This sequence is a bijection from N = [0..+oo) to Z = (-oo..+oo).

%H Rémy Sigrist, <a href="/A338241/b338241.txt">Table of n, a(n) for n = 0..6560</a>

%H Rémy Sigrist, <a href="/A338241/a338241.png">Scatterplot of the first 3^9 terms</a>

%F Sum_{k = 0..n} a(k) >= 0 with equality iff n belongs to A005823.

%e For n = 0:

%e - a(3*0) = 3*a(0),

%e - so a(0) = 0.

%e For n = 1:

%e - a(1) = 1 - 3*a(0) = 1.

%e For n = 2:

%e - a(2) = 3*a(0) - 1 = -1.

%e For n = 4:

%e - a(4) = 1 - 3*a(1) = -2.

%o (PARI) a(n) = { if (n==0, return (0), my (d=n%3, m=n\3); if (d==0, 3*a(m), d==1, 1-3*a(m), 3*a(m)-1)) }

%Y Cf. A005823, A117966, A338242-A338243 (bisections).

%K sign

%O 0,4

%A _Rémy Sigrist_, Oct 18 2020