A354047 A169683 read as ternary numbers.

0, 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 14, 15, 18, 27, 28, 29, 30, 31, 32, 33, 36, 37, 38, 39, 40, 41, 42, 45, 54, 81, 82, 83, 84, 85, 86, 87, 90, 91, 92, 93, 94, 95, 96, 99, 108, 109, 110, 111, 112, 113, 114, 117, 118, 119, 120, 121, 122, 123, 126, 135, 162

Offset: 0

Author

Jianing Song, May 16 2022

Keywords

• nonn
• base

Comments

a(0) = 0; if a(n) is of the form (3*m+2) * 3^r, then a(n+1) = (3*m+3) * 3^r, otherwise a(n+1) = a(n) + 1.

Viewed as a list, numbers whose ternary expansion contains only 0 and 1, except that the least significant nonzero digit can be 2.

Examples

			a(2^1-1..2^2-2) = a(0..2^1-1) + 3^0 = [1, 2];
a(2^2-1..2^3-2) = a(0..2^2-1) + 3^1 = [3, 4, 5, 6];
a(2^3-1..2^4-2) = a(0..2^3-1) + 3^2 = [9, 10, 11, 12, 13, 14, 15, 18];
a(2^4-1..2^5-2) = a(0..2^4-1) + 3^3 = [27, 28, 29, 30, 31, 32, 33, 36, 37, 38, 39, 40, 41, 42, 45, 54];
...
		

Links

• Jianing Song, Table of n, a(n) for n = 0..16382

Crossrefs

Cf. A169683.

Programs

PARI

A354047(lim) = my(v=vector(1<
				

Python

a, N = [0], 6   # generates terms 0..2**N-2
[[a.append(a[i] + 3**(n-1)) for i in range(2**n)] for n in range(1, N)]
print(a) # Michael S. Branicky, May 29 2022

Formula

a(0) = 0; for n >= 1, a(2^n-1+i) = a(i) + 3^(n-1) for 0 <= i <= 2^n-1.