A293208 - OEIS

%I #12 Oct 05 2017 09:54:08

%S 0,0,-2,-2,-1,-1,-4,-4,-2,-2,-3,-3,1,1,-1,-1,0,0,-3,-3,1,1,0,0,2,2,-2,

%T -2,-1,-1,-6,-6,-4,-4,-5,-5,1,1,0,0,2,2,-7,-7,-6,-6,-8,-8,3,3,2,2,4,4,

%U 1,1,2,2,-2,-2,-1,-1,-3,-3,0,0,-1,-1,2,2,-2,-2,3,3

%N Let b be the lexicographically earliest sequence of positive terms such that the function f defined by f(n) = Sum_{k=1..n} (i^k * b(k)) for any n >= 0 is injective (where i denotes the imaginary unit), and b(n) != b(n+1) and b() != b(n+2) for any n > 0; a(n) = real part of f(n).

%C See A293207 for the corresponding sequence b, and additional comments.

%H Rémy Sigrist, <a href="/A293208/b293208.txt">Table of n, a(n) for n = 0..59999</a>

%H Rémy Sigrist, <a href="/A293208/a293208.gp.txt">PARI program for A293208</a>

%e f(0) = 0, and a(0) = 0.

%e f(2) = f(1) + (i^1) * A293207(1) = 0 + (i) * 1 = i, and a(1) = 0.

%e f(3) = f(2) + (i^2) * A293207(2) = i + (-1) * 2 = -2 + i, and a(2) = -2.

%e f(4) = f(3) + (i^3) * A293207(3) = -2 + i + (-i) * 3 = -2 - 2*i, and a(3) = -2.

%e f(5) = f(4) + (i^4) * A293207(4) = -2 - 2*i + (1) * 1 = -1 - 2*i, and a(4) = -1.

%e f(6) = f(5) + (i^5) * A293207(5) = -1 - 2*i + (i) * 2 = -1, and a(5) = -1.

%e f(7) = f(6) + (i^6) * A293207(6) = -1 + (-1) * 3 = -4, and a(6) = -4.

%e f(8) = f(7) + (i^7) * A293207(7) = -4 + (-i) * 1 = -4 - i, and a(7) = -4.

%e f(9) = f(8) + (i^8) * A293207(8) = -4 - i + (1) * 2 = -2 - i, and a(8) = -2.

%e f(10) = f(9) + (i^9) * A293207(9) = -2 - i + (i) * 3 = -2 + 2*i, and a(9) = -2.

%e f(11) = f(10) + (i^10) * A293207(10) = -2 + 2*i + (-1) * 1 = -3 + 2*i, and a(10) = -3.

%o (PARI) See Links section.

%Y Cf. A293207.

%K sign,look

%O 0,3

%A _Rémy Sigrist_, Oct 02 2017