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A161674 Positions n such that A010060(n) + A010060(n+2) = 1. 8
0, 1, 4, 5, 6, 7, 8, 9, 12, 13, 16, 17, 20, 21, 22, 23, 24, 25, 28, 29, 30, 31, 32, 33, 36, 37, 38, 39, 40, 41, 44, 45, 48, 49, 52, 53, 54, 55, 56, 57, 60, 61, 64, 65, 68, 69, 70, 71, 72, 73, 76, 77, 80, 81, 84, 85, 86, 87, 88, 89, 92, 93, 94, 95, 96, 97, 100, 101, 102, 103, 104 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Locates patterns of the form 0x1 or 1x0 in the Thue-Morse sequence.
Complement to A081706. Also: union of sequences {2*A121539(n)+k}, k=0 or 1, generalized in A161673.
Also union of sequences {A079523(n)-k}, k=0 or 1. For a generalization see A161890. - Vladimir Shevelev, Jul 05 2009
The asymptotic density of this sequence is 2/3 (Rowland and Yassawi, 2015; Burns, 2016). - Amiram Eldar, Jan 30 2021
LINKS
Rob Burns, Asymptotic density of Motzkin numbers modulo small primes, arXiv:1611.04910 [math.NT], 2016.
Eric Rowland and Reem Yassawi, Automatic congruences for diagonals of rational functions, Journal de Théorie des Nombres de Bordeaux, Vol. 27, No. 1 (2015), pp. 245-288.
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 + 2] == 1, Sow[n]]]][[2, 1]] (* G. C. Greubel, Jan 05 2018 *)
Flatten[Position[Partition[ThueMorse[Range[0, 120]], 3, 1], _?(#[[1]]+#[[3]] == 1&), 1, Heads->False]]-1 (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 29 2019 *)
PROG
(PARI) is(n)=hammingweight(n)%2!=hammingweight(n+2)%2 \\ Charles R Greathouse IV, Aug 20 2013
CROSSREFS
Sequence in context: A039062 A067187 A321353 * A285623 A213518 A214419
KEYWORD
nonn,easy
AUTHOR
Vladimir Shevelev, Jun 16 2009
EXTENSIONS
Extended by R. J. Mathar, Aug 28 2009
STATUS
approved

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Last modified April 25 11:06 EDT 2024. Contains 371967 sequences. (Running on oeis4.)