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A271472 Binary representation of n in base i-1. 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 (list; graph; refs; listen; history; text; internal format)
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 = i-1. 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. Addison-Wesley, 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), 247-248.

LINKS

Chai Wah Wu, Table of n, a(n) for n = 0..10000

N. J. A. Sloane, Table of n, (I-1)^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

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Last modified August 23 14:00 EDT 2019. Contains 326229 sequences. (Running on oeis4.)