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A161817 Positions n such that A010060(n) = A010060(n+5). 6
0, 2, 5, 8, 10, 11, 12, 14, 15, 16, 18, 21, 24, 26, 29, 32, 34, 37, 40, 42, 43, 44, 46, 47, 48, 50, 53, 56, 58, 59, 60, 62, 63, 64, 66, 69, 72, 74, 75, 76, 78, 79, 80, 82, 85, 88, 90, 93, 96, 98, 101, 104, 106, 107, 108, 110, 111, 112, 114, 117, 120, 122, 125, 128, 130, 133, 136, 138, 139, 140, 142, 143, 144 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Let A=Axxxxxx be any sequence. Denote by A^* the intersection of A and the union of sequences {4*A(n)+k}, k=-1,0,1,2. Then the present sequence is the union of A079523^* and A121539^*.
Conjecture. In every sequence of numbers n such that A010060(n)=A010060(n+k) for fixed odd k, the odious (A000069) and evil (A001969) terms alternate. [Vladimir Shevelev, Jul 31 2009]
LINKS
J.-P. Allouche, Thue, Combinatorics on words, and conjectures inspired by the Thue-Morse sequence, J. de Théorie des Nombres de Bordeaux, 27, no. 2 (2015), 375-388.
V. Shevelev, Equations of the form t(x+a)=t(x) and t(x+a)=1-t(x) for Thue-Morse sequence, arXiv:0907.0880 [math.NT], 2009-2012.
MATHEMATICA
tm[0] = 0; tm[n_?EvenQ] := tm[n] = tm[n/2]; tm[n_] := tm[n] = 1 - tm[(n - 1)/2]; Reap[For[n = 0, n <= 20000, n++, If[tm[n] == tm[n + 5], Sow[n]]]][[2, 1]] (* G. C. Greubel, Jan 05 2018 *)
PROG
(PARI) is(n)=hammingweight(n+5)==Mod(hammingweight(n), 2) \\ Charles R Greathouse IV, Mar 26 2013
CROSSREFS
Sequence in context: A072476 A167541 A078345 * A080228 A153052 A352142
KEYWORD
nonn,base,easy
AUTHOR
Vladimir Shevelev, Jun 20 2009
STATUS
approved

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Last modified July 15 21:59 EDT 2024. Contains 374334 sequences. (Running on oeis4.)