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

1,3

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.

Links

Table of n, a(n) for n=1..47.

Example

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.

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]

Crossrefs

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

Sequence in context: A031402 A019438 A023798 * A362455 A062084 A331394

Adjacent sequences: A369632 A369633 A369634 * A369636 A369637 A369638

Keyword

nonn,base

Author

Clark Kimberling, Feb 26 2024

Status

approved