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A354047 A169683 read as ternary numbers. 2
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,base
AUTHOR
Jianing Song, May 16 2022
STATUS
approved

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Last modified May 29 00:29 EDT 2024. Contains 372921 sequences. (Running on oeis4.)