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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.
2
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, 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)
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 * A377430 A287323 A059985
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Jun 16 2021
STATUS
approved