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A248057
Positions of 1,1 in the Thue-Morse sequence (A010060).
4
2, 8, 14, 22, 26, 32, 38, 42, 50, 56, 62, 70, 74, 82, 88, 94, 98, 104, 110, 118, 122, 128, 134, 138, 146, 152, 158, 162, 168, 174, 182, 186, 194, 200, 206, 214, 218, 224, 230, 234, 242, 248, 254, 262, 266, 274, 280, 286, 290, 296, 302, 310, 314, 322, 328
OFFSET
1,1
COMMENTS
Every positive integer lies in exactly one of these four sequences: A248056, A091855, A091855, A248057.
LINKS
FORMULA
a(n) = 2*A091855(n) for n >= 1.
EXAMPLE
Thue-Morse sequence: 0,1,1,0,1,0,0,1,1,0,0,1,0,1,1,..., so that a(1) = 2 and a(2) = 8.
MATHEMATICA
z = 400; u = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {1, 0}}] &, {0}, 9] (* A010060 *)
v = Rest[u]
t1 = Table[If[u[[n]] == 0 && v[[n]] == 0, 1, 0], {n, 1, z}];
t2 = Table[If[u[[n]] == 0 && v[[n]] == 1, 1, 0], {n, 1, z}];
t3 = Table[If[u[[n]] == 1 && v[[n]] == 0, 1, 0], {n, 1, z}];
t4 = Table[If[u[[n]] == 1 && v[[n]] == 1, 1, 0], {n, 1, z}];
Flatten[Position[t1, 1]] (* A248056 *)
Flatten[Position[t2, 1]] (* A091855 *)
Flatten[Position[t3, 1]] (* A091785 *)
Flatten[Position[t4, 1]] (* A248057 *)
SequencePosition[ThueMorse[Range[400]], {1, 1}][[All, 2]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 16 2017 *)
PROG
(PARI) t(n)=hammingweight(n)%2;
for(n=1, 500, if(t(n)==1&&t(n-1)==1, print1(n, ", "))); \\ Joerg Arndt, Mar 12 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Sep 30 2014
STATUS
approved