A265210 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

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.

LINKS

Table of n, a(n) for n=0..83.

EXAMPLE

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

MATHEMATICA

(* Replace Flatten with Grid to display the triangle: *)

Flatten[Table[Reverse[IntegerDigits[2^n, 3]], {n, 0, 15}]]

PROG

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

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).

Sequence in context: A210682 A293433 A177025 * A023396 A091221 A106495

Adjacent sequences: A265207 A265208 A265209 * A265211 A265212 A265213

KEYWORD

nonn,tabf,base

AUTHOR

L. Edson Jeffery, Dec 04 2015

STATUS

approved