A292370 A binary encoding of the zeros in base-4 representation of n.

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

Offset

0,17

Links

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

Index entries for sequences related to binary expansion of n

Formula

For all n >= 0, A000120(a(n)) = A160380(n).

Example

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

Mathematica

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

Prog

(Scheme) (define (A292370 n) (if (zero? n) n (let loop ((n n) (b 1) (s 0)) (if (< n 4) s (let ((d (modulo n 4))) (if (zero? d) (loop (/ n 4) (+ b b) (+ s b)) (loop (/ (- n d) 4) (+ b b) s)))))))
(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==0 else '0' for i in k), 2)
print([a(n) for n in range(111)]) # Indranil Ghosh, Sep 21 2017

Crossrefs

Cf. A007088, A007090, A160380, A292371, A292372, A292373.

Cf. A291770 (analogous sequence for base-3).

Sequence in context: A075801 A243160 A272694 * A116943 A328389 A332789

Adjacent sequences: A292367 A292368 A292369 * A292371 A292372 A292373

Keyword

nonn,base

Author

Antti Karttunen, Sep 15 2017

Status

approved