A292371 A binary encoding of 1-digits in the base-4 representation of n.

0, 1, 0, 0, 2, 3, 2, 2, 0, 1, 0, 0, 0, 1, 0, 0, 4, 5, 4, 4, 6, 7, 6, 6, 4, 5, 4, 4, 4, 5, 4, 4, 0, 1, 0, 0, 2, 3, 2, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 3, 2, 2, 0, 1, 0, 0, 0, 1, 0, 0, 8, 9, 8, 8, 10, 11, 10, 10, 8, 9, 8, 8, 8, 9, 8, 8, 12, 13, 12, 12, 14, 15, 14, 14, 12, 13, 12, 12, 12, 13, 12, 12, 8, 9, 8, 8, 10, 11, 10, 10, 8, 9, 8, 8, 8, 9, 8, 8, 8

Offset

0,5

Links

Antti Karttunen, Table of n, a(n) for n = 0..65536

Rémy Sigrist, Interactive scatterplot of (a(n), A292372(n), A292373(n)) for n=0..4^8-1 [provided your web browser supports the Plotly library, you should see icons on the top right corner of the page: if you choose "Orbital rotation", then you will be able to rotate the plot alongside three axes, the 3D plot here corresponds to a Sierpiński triangle-based pyramid]

Index entries for sequences related to binary expansion of n

Formula

a(n) = A059905(A292272(n)) = A059905(n AND A003188(n)), where AND is bitwise-AND (A004198).

For all n >= 0, A000120(a(n)) = A160381(n).

Example

   n      a(n)     base-4(n)  binary(a(n))
                  A007090(n)  A007088(a(n))
  --      ----    ----------  ------------
   1        1          1           1
   2        0          2           0
   3        0          3           0
   4        2         10          10
   5        3         11          11
   6        2         12          10
   7        2         13          10
   8        0         20           0
   9        1         21           1
  10        0         22           0
  11        0         23           0
  12        0         30           0
  13        1         31           1
  14        0         32           0
  15        0         33           0
  16        4        100         100
  17        5        101         101
  18        4        102         100

Mathematica

Table[FromDigits[IntegerDigits[n, 4] /. k_ /; IntegerQ@ k :> If[k == 1, 1, 0], 2], {n, 0, 112}] (* Michael De Vlieger, Sep 21 2017 *)

Prog

(Scheme, with memoization-macro definec)
(definec (A292371 n) (if (zero? n) n (let ((d (modulo n 4))) (+ (if (= 1 d) 1 0) (* 2 (A292371 (/ (- n d) 4)))))))
(Python)
from sympy.ntheory.factor_ import digits
def a(n):
    k=digits(n, 4)[1:]
    return 0 if n==0 else int("".join('1' if i==1 else '0' for i in k), 2)
print([a(n) for n in range(116)]) # Indranil Ghosh, Sep 21 2017
(Python)
def A292371(n): return int(bin(n&~(n>>1))[:1:-2][::-1], 2) # Chai Wah Wu, Jun 30 2022

Crossrefs

Cf. A003188, A004198, A007088, A007090, A059905, A160381, A292272, A292370, A292372, A292373.

Cf. A289813 (analogous sequence for base 3).

Sequence in context: A090664 A086764 A255010 * A216683 A367896 A368123

Adjacent sequences: A292368 A292369 A292370 * A292372 A292373 A292374

Keyword

nonn,base

Author

Antti Karttunen, Sep 15 2017

Status

approved