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A232615
Variant of the Chandra-sutra (A014701) using 3 instead of 2, and a mod argument using residues 1 and 2.
0
0, 1, 1, 2, 2, 2, 3, 3, 2, 3, 3, 3, 4, 4, 3, 4, 4, 3, 4, 4, 4, 5, 5, 4, 5, 5, 3, 4, 4, 4, 5, 5, 4, 5, 5, 4, 5, 5, 5, 6, 6, 5, 6, 6, 4, 5, 5, 5, 6, 6, 5, 6, 6, 4, 5, 5, 5, 6, 6, 5, 6, 6, 5, 6, 6, 6, 7, 7, 6, 7, 7, 5, 6, 6, 6, 7, 7, 6, 7, 7, 4, 5, 5
OFFSET
1,4
COMMENTS
x :> x/3 if x == 0 mod 3, x :> x - x mod 3 otherwise. This sequence gives the number of steps needed to reach 0 or 1.
In base 3, number of 0's + (number of other digits - 1) * 2 + (1 if leading digit is 2).
LINKS
Eric Weisstein's World of Mathematics, Ternary.
EXAMPLE
8 -> 6 -> 2 -> 0.
28 -> 27 -> 9 -> 3 -> 1.
In base 3 the process is more obvious, e.g., 19 is 201 and the sequence is 201 -> 200 -> 20 -> 2 ->0, so a(19)=4. The number of zeros is 1, other digits is 2 and the leading digit is a 2, so we also have a(19) = 1 + (2-1)*2 + 1 = 4.
PROG
(JavaScript)
for (i=1; i<300; i++) {
c=0;
n=i;
while (n>1) {c++; m=n%3; if (m==0) n/=3; else n-=m; }
document.write(c+", ");
}
CROSSREFS
Cf. A014701.
Sequence in context: A212628 A272851 A242258 * A257177 A243423 A094528
KEYWORD
nonn,base
AUTHOR
Jon Perry, Nov 26 2013
STATUS
approved