A163543 -id:A163543 - cp's OEIS frontend

A163542 The relative direction (0=straight ahead, 1=turn right, 2=turn left) taken by the type I Hilbert's Hamiltonian walk A163357 at the step n.

1, 1, 2, 0, 2, 2, 1, 1, 2, 2, 0, 2, 1, 1, 0, 1, 2, 2, 1, 0, 1, 1, 2, 2, 1, 1, 0, 1, 2, 2, 0, 0, 2, 2, 1, 0, 1, 1, 2, 2, 1, 1, 0, 1, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 1, 2, 2, 0, 2, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 2, 1, 1, 0, 1, 2, 2, 0, 2, 1, 1, 2, 0, 2, 2, 1, 1, 2, 2, 0, 2, 1, 1, 0, 0, 1, 1, 2, 0, 2, 2

Offset: 1

Antti Karttunen, Aug 01 2009

nonn

a(16*n) = a(256*n) for all n.

Antti Karttunen, Table of n, a(n) for n = 1..65536

a(n) = A014681(A163543(n)). See also A163540.

HC = {L[n_ /; IntegerQ[n/2]] :> {F[n], L[n], L[n + 1], R[n + 2]},
   R[n_ /; IntegerQ[(n + 1)/2]] :> {F[n], R[n], R[n + 3], L[n + 2]},
   R[n_ /; IntegerQ[n/2]] :> {L[n], R[n + 1], R[n], F[n + 3]},
   L[n_ /; IntegerQ[(n + 1)/2]] :> {R[n], L[n + 3], L[n], F[n + 1]},
   F[n_ /; IntegerQ[n/2]] :> {L[n], R[n + 1], R[n], L[n + 3]},
   F[n_ /; IntegerQ[(n + 1)/2]] :> {R[n], L[n + 3], L[n], R[n + 1]}};
a[1] = L[0]; Map[(a[n_ /; IntegerQ[(n - #)/16]] :=
    Part[Flatten[a[(n + 16 - #)/16] /. HC /. HC], #]) &, Range[16]];
Part[a[#] & /@ Range[4^4] /. {L[] -> 2, R[] -> 1, F[_] -> 0},
2 ;; -1] (* Bradley Klee, Aug 07 2015 *)

(define (A163542 n) (A163241 (modulo (- (A163540 (1+ n)) (A163540 n)) 4)))

a(n) = A163241((A163540(n+1)-A163540(n)) modulo 4).

A163539 The change in Y-coordinate when moving from the n-1:th to the n-th term in the type I Hilbert's Hamiltonian walk A163357.

Original entry on oeis.org

0, 0, 1, 0, 1, 1, 0, -1, 0, 1, 0, -1, -1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, 1, 0, 1, 0, 0, -1, 0, 1, 1, 1, 0, -1, 0, 0, 1, 0, 1, 0, 1, 0, 0, -1, 0, 1, 0, 0, -1, 0, -1, -1, 0, 1, 0, -1, 0, 1, 1, 0, 1, 0, 1, 1, 0, -1, 0, 0, 1, 0, 1, 0, 1, 0, 0, -1, 0, 1, 1, 0, 1, 0, 1, 1, 0, -1, 0, 1, 0, -1, -1, 0

Offset: 0

Antti Karttunen, Aug 01 2009

sign

A. Karttunen, Table of n, a(n) for n = 0..65536

These are the first differences of A059252. See also: A163538, A163541, A163543.

a(0)=0, a(n) = A059252(n) - A059252(n-1).

A163541 The absolute direction (0=east, 1=south, 2=west, 3=north) taken by the type I Hilbert's Hamiltonian walk A163359 at the step n.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Aug 01 2009

nonn

Taking every sixteenth term gives the same sequence: (and similarly for all higher powers of 16 as well): a(n) = a(16*n).

Antti Karttunen, Table of n, a(n) for n = 1..4096

a(n) = A163541(A008598(n)) = A004442(A163540(n)). See also A163543.

HC = {L[n_ /; IntegerQ[n/2]] :> {F[n], L[n], L[n + 1], R[n + 2]},
R[n_ /; IntegerQ[(n + 1)/2]] :> {F[n], R[n], R[n + 3], L[n + 2]},
R[n_ /; IntegerQ[n/2]] :> {L[n], R[n + 1], R[n], F[n + 3]},
L[n_ /; IntegerQ[(n + 1)/2]] :> {R[n], L[n + 3], L[n], F[n + 1]},
F[n_ /; IntegerQ[n/2]] :> {L[n], R[n + 1], R[n], L[n + 3]},
F[n_ /; IntegerQ[(n + 1)/2]] :> {R[n], L[n + 3], L[n], R[n + 1]}};
a[1] = L[0]; Map[(a[n_ /; IntegerQ[(n - #)/16]] := Part[Flatten[a[(n + 16 - #)/16]/.HC/.HC],#]) &, Range[16]];
Part[FoldList[Mod[Plus[#1, #2], 4] &, 0, a[#] & /@ Range[4^4]/.{F[n_]:>0,L[n_]:>1,R[n_]:>-1}], 2 ;; -1] (* Bradley Klee, Aug 07 2015 *)

(define (A163541 n) (modulo (+ 3 (A163538 n) (A163539 n) (abs (A163538 n))) 4))

a(n) = A010873(A163538(n) + A163539(n) + abs(A163538(n)) + 3).

cp's OEIS Frontend

A163542 The relative direction (0=straight ahead, 1=turn right, 2=turn left) taken by the type I Hilbert's Hamiltonian walk A163357 at the step n.

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A163539 The change in Y-coordinate when moving from the n-1:th to the n-th term in the type I Hilbert's Hamiltonian walk A163357.

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Formula

A163541 The absolute direction (0=east, 1=south, 2=west, 3=north) taken by the type I Hilbert's Hamiltonian walk A163359 at the step n.

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