A161824 Numbers such that A010060(n) = A010060(n+6).

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

Offset: 1

Author

Vladimir Shevelev, Jun 20 2009

Keywords

• nonn
• base

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

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• J.-P. Allouche, Thue, Combinatorics on words, and conjectures inspired by the Thue-Morse sequence, arXiv:1401.3727 [math.NT], 2014.
• 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.

Crossrefs

Cf. A161817, A161674, A161673, A161639, A161641, A161627, A161579, A161580, A121539, A131323, A036554, A010060, A079523, A081706.

Programs

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 *)

PARI

is(n)=hammingweight(n)%2==hammingweight(n+6)%2 \\ Charles R Greathouse IV, Aug 20 2013

Extensions

Terms a(40) onwards added by G. C. Greubel, Jan 05 2018

Offset corrected by Mohammed Yaseen, Mar 29 2023