A019989 - OEIS

%I #33 Aug 01 2019 19:14:34

%S 2,5,6,8,14,15,16,18,20,23,24,26,35,41,42,43,45,47,48,49,52,54,56,59,

%T 60,62,68,69,70,72,74,77,78,80,91,98,104,105,107,116,122,123,124,126,

%U 128,129,130,133,135,137,140,141,142,144,146,147,148,154,156

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

%C 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

%H R. W. Gosper, J. Z. Hunts, <a href="https://www.gathering4gardner.org/g4g10gift/math/Gosper_Bill-Strange_Series_for_Sierpinskis_Gasket.pdf">Strange Series for Sierpinski’s Gasket</a>, G4G10 Exchange Book, Vol. 2 (2012), 59-60.

%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a019/A019989.java">Java program</a> (github)

%t 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];

%t 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}};

%t aR0[n_] := Flatten[Position[ Nest[Part[Flatten[# /. FractusRadius], 2 ;; -1] &, {0}, n], 0] - 1][[2 ;; -1]]/2; aR0[5](* _Bradley Klee_, Apr 16 2019 *)

%Y Cf. A019990, A019991, A307672.

%K nonn

%O 0,1

%A _Bill Gosper_

%E New name from _Sean A. Irvine_, Apr 30 2019