A292372 A binary encoding of 2-digits in base-4 representation of n.

0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 3, 2, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 3, 2, 0, 0, 1, 0, 4, 4, 5, 4, 4, 4, 5, 4, 6, 6, 7, 6, 4, 4, 5, 4, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 3, 2, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 3, 2, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 3, 2, 0, 0, 1, 0, 4, 4, 5, 4, 4, 4, 5, 4, 6, 6, 7, 6, 4, 4, 5, 4, 0, 0, 1, 0, 0, 0, 1, 0, 2

Offset

0,9

Links

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

Index entries for sequences related to binary expansion of n

Formula

a(n) = A059906(n AND A048724(n)), where AND is a bitwise-AND (A004198).

For all n >= 0, A000120(a(n)) = A160382(n).

Example

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

Mathematica

Table[FromDigits[IntegerDigits[n, 4] /. k_ /; IntegerQ@ k :> If[k == 2, 1, 0], 2], {n, 0, 120}] (* Michael De Vlieger, Sep 21 2017 *)

Prog

(Scheme, with memoization-macro definec)
(definec (A292372 n) (if (zero? n) n (let ((d (modulo n 4))) (+ (if (= 2 d) 1 0) (* 2 (A292372 (/ (- 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==2 else '0' for i in k), 2)
print([a(n) for n in range(121)]) # Indranil Ghosh, Sep 21 2017
(Python)
def A292372(n): return 0 if (m:=n&~(n<<1)) < 2 else int(bin(m)[-2:1:-2][::-1], 2) # Chai Wah Wu, Jun 30 2022

Crossrefs

Cf. A004198, A007088, A007090, A048724, A059906, A160382, A292370, A292371, A292373.

Cf. A289814 (analogous sequence for base-3).

Sequence in context: A022461 A306821 A271226 * A098008 A234808 A248079

Adjacent sequences: A292369 A292370 A292371 * A292373 A292374 A292375

Keyword

nonn,base

Author

Antti Karttunen, Sep 15 2017

Status

approved