A261185 Flowsnake parity pattern: a(n) = (A261180(n) mod 2).

0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1

Offset

1

Comments

This sequence is limit-periodic, thus it is somewhat similar to the Dragon Sequence A014577. Compare g.f. defining relations.

Links

Bradley Klee, Table of n, a(n) for n = 1..1000

Index entries for sequences that are fixed points of mappings

Formula

G.f. g(x) satisfies g(x) = x^(-3)*g(x^7) + (x^2 + x^3 + x^7)/(1 - x^7).

From Kevin Ryde, Oct 15 2022: (Start)

Fixed point of the morphism 0 -> 0,1,1,0,0,0,1, 1 -> 0,1,1,1,0,0,1 starting from 0.

a(n) = 1 iff n-1 written in base 7 has its least significant non-3 digit equal to 1 or 2 or 6.

(End)

Mathematica

a[x_ /; IntegerQ[(x + 3)/7]] :=  a[(x + 3)/7]; MapThread[(a[x_ /; IntegerQ[(x - #1)/7]] := #2) &, {{1, 2, 3, 5, 6, 7}, {0, 1, 1, 0, 0, 1}}]; a /@ Range[7^2]

Prog

(PARI) a(n) = n--; my(r); until(r!=3, [n, r]=divrem(n, 7)); bittest(70, r); \\ Kevin Ryde, Oct 15 2022

Crossrefs

Cf. A261180 (flowsnake directions), A007093 (base 7).

Cf. A014577, A261120.

Sequence in context: A359820 A241979 A200244 * A093692 A254114 A105384

Adjacent sequences: A261182 A261183 A261184 * A261186 A261187 A261188

Keyword

nonn,easy

Author

Bradley Klee, Aug 11 2015

Status

approved