The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A177505 Base 2i representation of n reinterpreted in base 4. 2
 0, 1, 2, 3, 304, 305, 306, 307, 288, 289, 290, 291, 272, 273, 274, 275, 256, 257, 258, 259, 560, 561, 562, 563, 544, 545, 546, 547, 528, 529, 530, 531, 512, 513, 514, 515, 816, 817, 818, 819, 800, 801, 802, 803, 784, 785 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The use of negabinary dispenses with the need for sign bits and for keeping track of signed and unsigned data types. Similarly, the use of base 2i, or quater-imaginary, dispenses with the need to represent the real and imaginary parts of a complex number separately. (The term "quater-imaginary" appears in Knuth's landmark book on computer programming). Quater-imaginary, based on the powers of 2i (twice the imaginary unit), uses the digits 0, 1, 2, 3. For purely real positive integers, the quater-imaginary representation is the same as negaquartal (base -4) except that 0's are "riffled" in, corresponding to the odd-indexed powers of 2i which are purely imaginary numbers. Therefore, to obtain the base 2i representations of positive real numbers, the algorithm for base -4 representations can be employed with only a small adjustment. To obtain the base 2i representation of a complex number a+bi, do as above for the real part, then again for the real part of 2i*(a+bi) = -2b+2ai, giving the digits corresponding to the odd-indexed powers of 2i. - Daniel Forgues, May 18 2012 REFERENCES Donald Knuth, The Art of Computer Programming. Volume 2, 2nd Edition. Reading, Massachussetts: Addison-Wesley (1981): 189 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Donald Knuth, An imaginary number system, Communications of the ACM 3 (4), April 1960, pp. 245-247. OEIS Wiki, Quater-imaginary base Wikipedia, Quater-imaginary base FORMULA Conjectures from Colin Barker, Jul 16 2019: (Start) G.f.: x*(1 + x + x^2 + 301*x^3 + x^4 + x^5 + x^6 - 19*x^7 + x^8 + x^9 + x^10 - 19*x^11 + x^12 + x^13 + x^14 - 19*x^15) / ((1 - x)^2*(1 + x)*(1 + x^2)*(1 + x^4)*(1 + x^8)). a(n) = a(n-1) + a(n-16) - a(n-17) for n>16. (End) EXAMPLE a(5) = 305 because 5 in base 2i is 10301 ( = (2i)^4 + 3 * (2i)^2 + (2i)^0), and (-4)^4 + 3 * (-4)^2 + (-4)^0 = 256 + 3 * 16 + 1 = 305. MATHEMATICA (* First run the program from A039724 to define ToNegaBases *) Table[FromDigits[Riffle[IntegerDigits[ToNegaBases[n, 4]], 0], 4], {n, 0, 63}] CROSSREFS Cf. A005351 (base -2 representation of n reinterpreted as binary). Cf. A212494 (base 2i representation of n). Sequence in context: A087313 A004876 A307212 * A068104 A065586 A110931 Adjacent sequences:  A177502 A177503 A177504 * A177506 A177507 A177508 KEYWORD nonn,easy,base AUTHOR Alonso del Arte, Feb 03 2012 STATUS approved

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

Last modified November 27 18:14 EST 2020. Contains 338683 sequences. (Running on oeis4.)