login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A066321 Binary representation of base i-1 expansion of n: replace i-1 by 2 in base i-1 expansion of n. 7
0, 1, 12, 13, 464, 465, 476, 477, 448, 449, 460, 461, 272, 273, 284, 285, 256, 257, 268, 269, 3280, 3281, 3292, 3293, 3264, 3265, 3276, 3277, 3088, 3089, 3100, 3101, 3072, 3073, 3084, 3085, 3536, 3537, 3548, 3549, 3520, 3521, 3532, 3533, 3344, 3345, 3356 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Here i = sqrt(-1).

First differences follow a strange period-16 pattern: 1 11 1 XXX 1 11 1 -29 1 11 1 -189 1 11 1 -29 where XXX is given by A066322. Number of one-bits is A066323.

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

Paul Tek, Table of n, a(n) for n = 0..10000

Paul Tek, Perl program for this sequence

N. J. A. Sloane, Table of n, (I-1)^n for n=0..100

FORMULA

In "rebase notation" a(n) = (i-1)[n]2.

EXAMPLE

a(4) = 464 = 2^8+2^7+2^6+2^4 since (i-1)^8+(i-1)^7+(i-1)^6+(i-1)^4 = 4.

PROG

(Perl) See Links section.

(Python)

from gmpy2 import c_divmod

u = ('0000', '1000', '0011', '1011')

def A066321(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], 2) # Chai Wah Wu, Apr 09 2016

CROSSREFS

Cf. A066322, A066323.

See A271472 for the conversion of these decimal numbers to binary.

See A009116 and A009545 for real and imaginary parts of (i-1)^n (except for signs).

Sequence in context: A041309 A041310 A275959 * A099415 A042293 A061097

Adjacent sequences:  A066318 A066319 A066320 * A066322 A066323 A066324

KEYWORD

base,easy,nonn

AUTHOR

Marc LeBrun, Dec 14 2001

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified September 28 09:55 EDT 2016. Contains 276601 sequences.