A232615 Variant of the Chandra-sutra (A014701) using 3 instead of 2, and a mod argument using residues 1 and 2.

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

Author

Jon Perry, Nov 26 2013

Keywords

• nonn
• base

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).

Examples

			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.
		

Links

• Eric Weisstein's World of Mathematics, Ternary.
• Wikipedia, Ternary numeral system

Crossrefs

Cf. A014701.

Programs

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+", ");
}