

A271472


Binary representation of n in base i1.


3



0, 1, 1100, 1101, 111010000, 111010001, 111011100, 111011101, 111000000, 111000001, 111001100, 111001101, 100010000, 100010001, 100011100, 100011101, 100000000, 100000001, 100001100, 100001101, 110011010000, 110011010001, 110011011100, 110011011101, 110011000000, 110011000001
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OFFSET

0,3


COMMENTS

This is A066321(n) converted from base 10 to base 2.
Every Gaussian integer r+s*i (r, s ordinary integers) has a unique representation as a sum of powers of t = i1. For example 3 = 1+b^2+b^3, that is, "1101" in binary, which explains a(3) = 1101. See A066321 for further information.


REFERENCES

D. E. Knuth, The Art of Computer Programming. AddisonWesley, Reading, MA, 1969, Vol. 2, p. 172. (See also exercise 16, p. 177; answer, p. 494.)
W. J. Penney, A "binary" system for complex numbers, JACM 12 (1965), 247248.


LINKS

Chai Wah Wu, Table of n, a(n) for n = 0..10000
N. J. A. Sloane, Table of n, (I1)^n for n=0..100


PROG

(Python)
from gmpy2 import c_divmod
u = ('0000', '1000', '0011', '1011')
def A271472(n):
if n == 0:
return 0
else:
s, q = '', n
while q:
q, r = c_divmod(q, 4)
s += u[r]
return int(s[::1]) # Chai Wah Wu, Apr 09 2016


CROSSREFS

Cf. A066321.
Sequence in context: A280612 A281039 A078199 * A147816 A050926 A083933
Adjacent sequences: A271469 A271470 A271471 * A271473 A271474 A271475


KEYWORD

nonn,base


AUTHOR

N. J. A. Sloane, Apr 08 2016


STATUS

approved



