A265210 Irregular triangle read by rows in which row n lists the base 3 digits of 2^n in reverse order, n >= 0.

1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 1, 0, 1, 1, 0, 1, 2, 2, 0, 2, 1, 1, 1, 1, 1, 0, 0, 1, 2, 2, 2, 0, 0, 2, 1, 2, 2, 1, 0, 1, 1, 2, 1, 2, 0, 1, 2, 2, 1, 0, 2, 1, 2, 1, 2, 1, 2, 0, 1, 0, 2, 0, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1

Offset: 0

Author

L. Edson Jeffery, Dec 04 2015

Keywords

• nonn
• tabf
• base

Comments

The length of row n is A020915(n) = 1 + A136409(n).

Conjecture 1: The sequence in column k is periodic, with period p(k) = 2*3^(k-1) = A008776(k-1), k >= 1, and in which the numbers 0,1,2 appear with equal frequency, for each k>1.

Examples

			n
0:    1
1:    2
2:    1  1
3:    2  2
4:    1  2  1
5:    2  1  0  1
6:    1  0  1  2
7:    2  0  2  1  1
8:    1  1  1  0  0  1
9:    2  2  2  0  0  2
10:   1  2  2  1  0  1  1
11:   2  1  2  0  1  2  2
12:   1  0  2  1  2  1  2  1
13:   2  0  1  0  2  0  2  0  1
14:   1  1  2  0  1  1  1  1  2
15:   2  2  1  1  2  2  2  2  1  1
		

Crossrefs

Cf. A000079 (powers of 2), A004642 (powers of 2 written in base 3), A008776 (2*3^n).

Cf. A265209 (base 3 digits of 2^n).

Cf. A264980 (row n read as ternary number).

Cf. A037096 (numbers constructed from the inverse case, base 2 digits of 3^n).

Programs

Mathematica

(* Replace Flatten with Grid to display the triangle: *)
Flatten[Table[Reverse[IntegerDigits[2^n, 3]], {n, 0, 15}]]

PARI

A265210_row(n)=Vecrev(digits(2^n,3)) \\ M. F. Hasler, Dec 05 2015