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A292371 A binary encoding of 1-digits in the base-4 representation of n. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

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) = 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(map(a, range(116))) # Indranil Ghosh, Sep 21 2017

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 A323326 A274884

Adjacent sequences:  A292368 A292369 A292370 * A292372 A292373 A292374

KEYWORD

nonn,base

AUTHOR

Antti Karttunen, Sep 15 2017

STATUS

approved

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Last modified January 17 18:14 EST 2020. Contains 330987 sequences. (Running on oeis4.)