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

1,3

Comments

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).

Links

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

Formula

A053735(a(m) * a(n)) = A053735(a(m)) * A053735(a(n)).

Prog

(PARI) See Links section.

Crossrefs

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

Sequence in context: A344297 A344292 A356823 * A287323 A059985 A137709

Adjacent sequences: A345356 A345357 A345358 * A345360 A345361 A345362

Keyword

nonn,base

Author

Rémy Sigrist, Jun 16 2021

Status

approved