A369635 - OEIS

%I #27 Mar 02 2024 13:24:43

%S 0,1,2,3,5,6,7,11,15,19,21,34,46,59,65,102,140,177,202,308,420,532,

%T 606,925,1261,1598,1820,2775,3785,4794,5467,8327,11355,14383,16401,

%U 24982,34066,43151,49205,74946,102200,129453,147622,224840,306600,388360,442866

%N Numbers in whose base 3-representation every two consecutive digits and every three consecutive digits are distinct.

%C In other words, the ternary expansion of the number does not contain any string xx or xxx.

%C The first eleven terms of this sequence comprise the base-3 xenodrome, A023798.

%C Ordered union of {0}, A037496, A037504, A037512, and A037520.

%e The base-3 representation of 7 is 21, in which every two consecutive digits are distinct, so 7 is a term of the sequence.

%e The base-3 representation of 532 is 201201, in which every 3 consecutive digits are distinct, so 532 is a term of the sequence.

%t s1 = LinearRecurrence[{3, 0, 1, -3}, {0, 1, 3, 11}, 30]  (* A037496 *)

%t s2 = LinearRecurrence[{3, 0, 1, -3}, {0, 1, 5, 15}, 30]  (* A037504 *)

%t s3 = LinearRecurrence[{3, 0, 1, -3}, {0, 2, 6, 19}, 30]  (* A037512 *)

%t s4 = LinearRecurrence[{3, 0, 1, -3}, {0, 7, 21, 65}, 30] (* A037520 *)

%t s = Union[s1, s2, s3, s4]

%Y Cf. A023798, A037496, A037504, A037512, and A037520.

%K nonn,base

%O 1,3

%A _Clark Kimberling_, Feb 26 2024