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A305392 First differences of A140100. 8
2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) seems to take only the values 1 or 2, where {a(n), a(n+1)} may be {2, 1} or {1, 2} or {2, 2}, but not {1, 1}, and where {a(n), a(n+1), a(n+2), a(n+3)} may be {2, 1, 2, 1} or {1, 2, 1, 2} or {1, 2, 2, 1}, but not {2, 1, 1, 2}. The second differences of A140100 (first differences of this sequence) thus seem to take only the values -1 or 0 or 1. - Daniel Forgues, Aug 17 2018

From Michel Dekking, Mar 16 2019: (Start)

Let x be the tribonacci word x = A092782 = 1,2,1,3,1,2,1,1,...

Consider the morphism delta:

      1 -> 2212121212121,

      2 -> 22121212121,

      3 -> 2212121.

Conjecture: (a(n)) =  212121 delta(x).

(End)

Conjecture: This sequence (prefixed by 1 since A140100 should really begin with 0) is 1.TTW(2,1,1) where TTW is the ternary tribonacci word defined in A080843,  or equally it is THETA(2,1,1), where THETA is defined in A275925. - N. J. A. Sloane, Mar 19 2019

All these conjectures are now theorems - see the Dekking et al. paper. - N. J. A. Sloane, Jul 22 2019

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..49999

F. Michel Dekking, Jeffrey Shallit, and N. J. A. Sloane, Queens in exile: non-attacking queens on infinite chess boards, arXiv:1907.09120, July 2019

FORMULA

a(n) = A140100(n+1)-A140100(n).

CROSSREFS

For first differences of A140100, A140101, A140102, A140103 see A305392, A305374, A305393, A305394.

Sequence in context: A193453 A227944 A095772 * A175301 A214074 A003640

Adjacent sequences:  A305389 A305390 A305391 * A305393 A305394 A305395

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 23 2018

STATUS

approved

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Last modified January 22 04:27 EST 2020. Contains 331133 sequences. (Running on oeis4.)