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

0,3

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.

Links

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

Formula

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

Example

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];
...

Prog

(PARI) A354047(lim) = my(v=vector(1<<lim-1)); v[1] = 0; for(n=1, lim-1, for(i=0, 1<<n-1, v[1<<n+i] = v[i+1]+3^(n-1))); v \\ gives a(0..2^lim-2)
(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

Crossrefs

Cf. A169683.

Sequence in context: A272574 A039111 A037475 * A031487 A047422 A340152

Adjacent sequences: A354044 A354045 A354046 * A354048 A354049 A354050

Keyword

nonn,base

Author

Jianing Song, May 16 2022

Status

approved