A345358 -id:A345358 - cp's OEIS frontend

A345359 Lexicographically earliest sequence of distinct nonnegative integers such that the product of two terms, not necessarily distinct, can be computed without carry in base 3.

0, 1, 3, 4, 9, 10, 12, 27, 28, 30, 31, 36, 81, 82, 84, 85, 90, 93, 108, 243, 244, 246, 247, 252, 253, 255, 270, 279, 324, 729, 730, 732, 733, 738, 739, 741, 756, 759, 765, 810, 837, 972, 2187, 2188, 2190, 2191, 2196, 2197, 2199, 2214, 2215, 2217, 2218, 2223

Offset: 1

Rémy Sigrist, Jun 16 2021

All terms belong to A005836.
If m is a term, then 3*m is also a term (in particular, all powers of 3 appear in the sequence).
The representation of the 1's in the ternary expansion of consecutive terms has interesting features (see illustration in Links section).

Rémy Sigrist, Table of n, a(n) for n = 1..2500
Rémy Sigrist, Binary plot of (n, A289831(a(n))) for n = 1..255 (representation of the 1's in the ternary expansion of the first 255 terms)
Rémy Sigrist, PARI program for A345359

Cf. A005836, A053735, A131577 (binary analog), A289831, A345358 (decimal analog).

PARI
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See Links section.
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A053735(a(m) * a(n)) = A053735(a(m)) * A053735(a(n)).

cp's OEIS Frontend

A345359 Lexicographically earliest sequence of distinct nonnegative integers such that the product of two terms, not necessarily distinct, can be computed without carry in base 3.

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