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A161824 Numbers such that A010060(n) = A010060(n+6). 5
0, 1, 2, 3, 6, 7, 8, 9, 12, 13, 16, 17, 18, 19, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33, 34, 35, 38, 39, 40, 41, 44, 45, 48, 49, 50, 51, 54, 55, 56, 57, 60, 61, 64, 65, 66, 67, 70, 71, 72, 73, 76, 77, 80, 81, 82, 83, 86, 87, 88, 89, 90, 91, 94, 95, 96, 97, 98, 99, 102, 103, 104, 105, 108 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Let A=Axxxxxx be any sequence from OEIS. Denote by A^* the intersection of the union of sequences {2*A(n)+j}, j=0,1, and the union of sequences {4*A(n)+k}, k=-2,-1,0,1. Then the sequence is the union of (A079523)^* and (A121539)^*.
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.
Vladimir 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 <= 6000, n++, If[tm[n] == tm[n + 6], Sow[n]]]][[2, 1]] (* G. C. Greubel, Jan 05 2018 *)
PROG
(PARI) is(n)=hammingweight(n)%2==hammingweight(n+6)%2 \\ Charles R Greathouse IV, Aug 20 2013
CROSSREFS
Sequence in context: A039029 A037460 A285134 * A102806 A275884 A003605
KEYWORD
nonn,base
AUTHOR
Vladimir Shevelev, Jun 20 2009
EXTENSIONS
Terms a(40) onwards added by G. C. Greubel, Jan 05 2018
Offset corrected by Mohammed Yaseen, Mar 29 2023
STATUS
approved

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Last modified June 20 21:09 EDT 2024. Contains 373532 sequences. (Running on oeis4.)