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A292372 A binary encoding of 2-digits in base-4 representation of n. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified July 28 17:15 EDT 2021. Contains 346335 sequences. (Running on oeis4.)