A292373 A binary encoding of 3-digits in base-4 representation of n.

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

Offset

0,13

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(A048735(n)) = A059906(A213370(n)).

For all n >= 0, A000120(a(n)) = A160383(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        1          3           1
   4        0         10           0
   5        0         11           0
   6        0         12           0
   7        1         13           1
   8        0         20           0
   9        0         21           0
  10        0         22           0
  11        1         23           1
  12        2         30          10
  13        2         31          10
  14        2         32          10
  15        3         33          11
  16        0        100           0
  17        0        101           0
  18        0        102           0
  19        1        103           1

Prog

(Scheme, with memoization-macro definec)
(definec (A292373 n) (if (zero? n) n (let ((d (modulo n 4))) (+ (if (= 3 d) 1 0) (* 2 (A292373 (/ (- n d) 4)))))))
(Python)
def A292373(n): return int(bin(n&n>>1)[:1:-2][::-1], 2) # Chai Wah Wu, Jun 30 2022

Crossrefs

Cf. A007088, A007090, A048735, A059905, A059906, A160383, A213370, A292370, A292371, A292372.

Sequence in context: A235812 A343471 A035307 * A305383 A004481 A307296

Adjacent sequences: A292370 A292371 A292372 * A292374 A292375 A292376

Keyword

nonn,base

Author

Antti Karttunen, Sep 15 2017

Status

approved