OFFSET
0,2
COMMENTS
This sequence can be also computed with a recurrence that does not explicitly refer to 3^n. See the C program.
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media Inc., (2002), p. 119.
LINKS
Antti Karttunen, Table of n, a(n) for n = 0..11
Antti Karttunen, C program for computing this sequence.
FORMULA
EXAMPLE
When powers of 3 are written in binary (see A004656), under each other as:
000000000001 (1)
000000000011 (3)
000000001001 (9)
000000011011 (27)
000001010001 (81)
000011110011 (243)
001011011001 (729)
100010001011 (2187)
it can be seen that the bits in the n-th column from the right can be arranged in periods of 2^n: 1, 2, 4, 8, ... This sequence is formed from those bits: 1, is binary for 1, thus a(0) = 1. 01, reversed is 10, which is binary for 2, thus a(1) = 2, 0000 is binary for 0, thus a(2)=0, 000110011, reversed is 11001100 = A007088(204), thus a(3) = 204.
MAPLE
a(n) := sum( 'bit_n(3^i, n)*(2^i)', 'i'=0..(2^(n))-1);
bit_n := (x, n) -> `mod`(floor(x/(2^n)), 2);
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Jan 29 1999
EXTENSIONS
Entry revised by Antti Karttunen, Dec 29 2007
Name changed and the example corrected by Antti Karttunen, Dec 05 2015
STATUS
approved