A369635 Numbers in whose base 3-representation every two consecutive digits and every three consecutive digits are distinct.

0, 1, 2, 3, 5, 6, 7, 11, 15, 19, 21, 34, 46, 59, 65, 102, 140, 177, 202, 308, 420, 532, 606, 925, 1261, 1598, 1820, 2775, 3785, 4794, 5467, 8327, 11355, 14383, 16401, 24982, 34066, 43151, 49205, 74946, 102200, 129453, 147622, 224840, 306600, 388360, 442866

Offset: 1

Author

Clark Kimberling, Feb 26 2024

Keywords

• nonn
• base

Comments

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

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

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

Examples

			The base-3 representation of 7 is 21, in which every two consecutive digits are distinct, so 7 is a term of the sequence.
The base-3 representation of 532 is 201201, in which every 3 consecutive digits are distinct, so 532 is a term of the sequence.
		

Crossrefs

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

Programs

Mathematica

s1 = LinearRecurrence[{3, 0, 1, -3}, {0, 1, 3, 11}, 30]  (* A037496 *)
s2 = LinearRecurrence[{3, 0, 1, -3}, {0, 1, 5, 15}, 30]  (* A037504 *)
s3 = LinearRecurrence[{3, 0, 1, -3}, {0, 2, 6, 19}, 30]  (* A037512 *)
s4 = LinearRecurrence[{3, 0, 1, -3}, {0, 7, 21, 65}, 30] (* A037520 *)
s = Union[s1, s2, s3, s4]