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A binary encoding of 1-digits in the base-4 representation of n.
7

%I #41 Jun 30 2022 14:43:59

%S 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,

%T 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,

%U 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

%N A binary encoding of 1-digits in the base-4 representation of n.

%H Antti Karttunen, <a href="/A292371/b292371.txt">Table of n, a(n) for n = 0..65536</a>

%H Rémy Sigrist, <a href="https://practical-ardinghelli-959d8f.netlify.app/a292371">Interactive scatterplot of (a(n), A292372(n), A292373(n)) for n=0..4^8-1</a> [provided your web browser supports the Plotly library, you should see icons on the top right corner of the page: if you choose "Orbital rotation", then you will be able to rotate the plot alongside three axes, the 3D plot here corresponds to a Sierpiński triangle-based pyramid]

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%F a(n) = A059905(A292272(n)) = A059905(n AND A003188(n)), where AND is bitwise-AND (A004198).

%F For all n >= 0, A000120(a(n)) = A160381(n).

%e n a(n) base-4(n) binary(a(n))

%e A007090(n) A007088(a(n))

%e -- ---- ---------- ------------

%e 1 1 1 1

%e 2 0 2 0

%e 3 0 3 0

%e 4 2 10 10

%e 5 3 11 11

%e 6 2 12 10

%e 7 2 13 10

%e 8 0 20 0

%e 9 1 21 1

%e 10 0 22 0

%e 11 0 23 0

%e 12 0 30 0

%e 13 1 31 1

%e 14 0 32 0

%e 15 0 33 0

%e 16 4 100 100

%e 17 5 101 101

%e 18 4 102 100

%t Table[FromDigits[IntegerDigits[n, 4] /. k_ /; IntegerQ@ k :> If[k == 1, 1, 0], 2], {n, 0, 112}] (* _Michael De Vlieger_, Sep 21 2017 *)

%o (Scheme, with memoization-macro definec)

%o (definec (A292371 n) (if (zero? n) n (let ((d (modulo n 4))) (+ (if (= 1 d) 1 0) (* 2 (A292371 (/ (- n d) 4)))))))

%o (Python)

%o from sympy.ntheory.factor_ import digits

%o def a(n):

%o k=digits(n, 4)[1:]

%o return 0 if n==0 else int("".join('1' if i==1 else '0' for i in k), 2)

%o print([a(n) for n in range(116)]) # _Indranil Ghosh_, Sep 21 2017

%o (Python)

%o def A292371(n): return int(bin(n&~(n>>1))[:1:-2][::-1],2) # _Chai Wah Wu_, Jun 30 2022

%Y Cf. A003188, A004198, A007088, A007090, A059905, A160381, A292272, A292370, A292372, A292373.

%Y Cf. A289813 (analogous sequence for base 3).

%K nonn,base

%O 0,5

%A _Antti Karttunen_, Sep 15 2017