A037504 -id:A037504 - cp's OEIS frontend

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

Clark Kimberling, Feb 26 2024

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.

			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.

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

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]

cp's OEIS Frontend

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

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