A293208 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).

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, -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, 1, 1, 2, 2, -2, -2, -1, -1, -3, -3, 0, 0, -1, -1, 2, 2, -2, -2, 3, 3

Offset

0,3

Comments

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

Links

Rémy Sigrist, Table of n, a(n) for n = 0..59999

Rémy Sigrist, PARI program for A293208

Example

f(0) = 0, and a(0) = 0.
f(2) = f(1) + (i^1) * A293207(1) = 0 + (i) * 1 = i, and a(1) = 0.
f(3) = f(2) + (i^2) * A293207(2) = i + (-1) * 2 = -2 + i, and a(2) = -2.
f(4) = f(3) + (i^3) * A293207(3) = -2 + i + (-i) * 3 = -2 - 2*i, and a(3) = -2.
f(5) = f(4) + (i^4) * A293207(4) = -2 - 2*i + (1) * 1 = -1 - 2*i, and a(4) = -1.
f(6) = f(5) + (i^5) * A293207(5) = -1 - 2*i + (i) * 2 = -1, and a(5) = -1.
f(7) = f(6) + (i^6) * A293207(6) = -1 + (-1) * 3 = -4, and a(6) = -4.
f(8) = f(7) + (i^7) * A293207(7) = -4 + (-i) * 1 = -4 - i, and a(7) = -4.
f(9) = f(8) + (i^8) * A293207(8) = -4 - i + (1) * 2 = -2 - i, and a(8) = -2.
f(10) = f(9) + (i^9) * A293207(9) = -2 - i + (i) * 3 = -2 + 2*i, and a(9) = -2.
f(11) = f(10) + (i^10) * A293207(10) = -2 + 2*i + (-1) * 1 = -3 + 2*i, and a(10) = -3.

Prog

(PARI) See Links section.

Crossrefs

Cf. A293207.

Sequence in context: A140643 A331409 A108017 * A247364 A301895 A229054

Adjacent sequences: A293205 A293206 A293207 * A293209 A293210 A293211

Keyword

sign,look

Author

Rémy Sigrist, Oct 02 2017

Status

approved