A333384 Use the Möbius (or Moebius) function mu(n) (A008683) to define a walk on a square lattice. A value of 1 is a move to the right, a value of -1 is a move to the left, and a value of 0 is a move either up or down depending on whether the previous nonzero value was +1 or -1. Sequence lists moves which reach a point that is further from the origin than any earlier move.

0, 1, 4, 5, 8, 9, 12, 13, 20, 24, 25, 48, 49, 50, 73, 84, 100, 103, 104, 105, 108, 109, 110, 200, 243, 244, 245, 246, 273, 620, 621, 646, 647, 648, 653, 654, 661, 664, 665, 666, 2655, 2656, 2803, 2804, 2837, 3212, 3213, 3214, 3215, 3216, 3227, 3228, 3231, 3232, 3233, 3234, 3235

Offset

1,3

Links

Table of n, a(n) for n=1..57.

Example

a(6) is 9. a(5) has a position on the Cartesian plane {-2, -2} and Möbius mu(9) is 0 and the previous nonzero was -1, resulted in a position of {-2, -3}; a distance further from the origin than a(5).

Mathematica

k = 1; flg = mxd = ns = ew = 0; lst = {0}; While[k < 1001, mu = MoebiusMu@ k; If[ Abs[mu] > 0, flg = mu; ns = ns + mu, ew = ew + flg]; d = ns^2 + ew^2; If[mxd < d, mxd = d; AppendTo[lst, k]]; k++]; lst

Crossrefs

Cf. A002321, A008683.

Sequence in context: A338062 A126001 A321333 * A334992 A269984 A188085

Adjacent sequences: A333381 A333382 A333383 * A333385 A333386 A333387

Keyword

easy,nonn

Author

Hayden H. Rigdon and Robert G. Wilson v, Mar 18 2020

Status

approved