A019989 Indices n such that A307672(2*n) = 0.

2, 5, 6, 8, 14, 15, 16, 18, 20, 23, 24, 26, 35, 41, 42, 43, 45, 47, 48, 49, 52, 54, 56, 59, 60, 62, 68, 69, 70, 72, 74, 77, 78, 80, 91, 98, 104, 105, 107, 116, 122, 123, 124, 126, 128, 129, 130, 133, 135, 137, 140, 141, 142, 144, 146, 147, 148, 154, 156

Offset: 0

Author

Bill Gosper

Keywords

• nonn

Comments

The original definition was: "A threequence, a 3-way partitioning of the integers: define a,b,c,A,B,C by a(0)=true, b(0)=c(0)=A(0)=B(0)=C(0)=false, a(n)=a(m) OR C(m) OR B(m), b(n)= b(m) OR A(m) OR C(m), c(n)= c(m) OR B(m) OR A(m), A(n)= A(m) OR b(m) OR c(m), B(n)= B(m) OR c(m) OR a(m), C(n)= C(m) OR a(m) OR b(m), where m = [ (n+1)/3 ]; sequence gives n such that a(2n) is true." - Bradley Klee, Apr 16 2019

Links

• R. W. Gosper, J. Z. Hunts, Strange Series for Sierpinski’s Gasket, G4G10 Exchange Book, Vol. 2 (2012), 59-60.
• Sean A. Irvine, Java program (github)

Crossrefs

Cf. A019990, A019991, A307672.

Programs

Mathematica

iterate[sets_] := With[{ind = {{1, 5, 6}, {2, 6, 4}, {3, 4, 5}, {4, 3, 2}, {5, 1, 3}, {6, 2, 1}} }, Union @@ (3*sets[[#]] + {0, -1, 1}) & /@ ind];
Part[Union @@ # & /@ Transpose[NestList[iterate, Append[Table[{}, 5], {1}], 10]], 1, 1 ;; 59]/2 (* Bradley Klee, Apr 15 2019 *) FractusRadius = {0 -> {4, 0, 5}, 1 -> {5, 1, 3}, 2 -> {3, 2, 4}, 3 -> {2, 3, 1}, 4 -> {0, 4, 2}, 5 -> {1, 5, 0}};
aR0[n_] := Flatten[Position[ Nest[Part[Flatten[# /. FractusRadius], 2 ;; -1] &, {0}, n], 0] - 1][[2 ;; -1]]/2; aR0[5](* Bradley Klee, Apr 16 2019 *)

Extensions

New name from Sean A. Irvine, Apr 30 2019