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A binary encoding of 2-digits in base-4 representation of n.
6

%I #25 Jun 30 2022 14:44:03

%S 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,

%T 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,

%U 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

%N A binary encoding of 2-digits in base-4 representation of n.

%H Antti Karttunen, <a href="/A292372/b292372.txt">Table of n, a(n) for n = 0..65536</a>

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

%F a(n) = A059906(n AND A048724(n)), where AND is a bitwise-AND (A004198).

%F For all n >= 0, A000120(a(n)) = A160382(n).

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

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

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

%e 1 0 1 0

%e 2 1 2 1

%e 3 0 3 0

%e 4 0 10 0

%e 5 0 11 0

%e 6 1 12 1

%e 7 0 13 0

%e 8 2 20 10

%e 9 2 21 10

%e 10 3 22 11

%e 11 2 23 10

%e 12 0 30 0

%e 13 0 31 0

%e 14 1 32 1

%e 15 0 33 0

%e 16 0 100 0

%e 17 0 101 0

%e 18 1 102 1

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

%o (Scheme, with memoization-macro definec)

%o (definec (A292372 n) (if (zero? n) n (let ((d (modulo n 4))) (+ (if (= 2 d) 1 0) (* 2 (A292372 (/ (- 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==2 else '0' for i in k), 2)

%o print([a(n) for n in range(121)]) # _Indranil Ghosh_, Sep 21 2017

%o (Python)

%o def A292372(n): return 0 if (m:=n&~(n<<1)) < 2 else int(bin(m)[-2:1:-2][::-1],2) # _Chai Wah Wu_, Jun 30 2022

%Y Cf. A004198, A007088, A007090, A048724, A059906, A160382, A292370, A292371, A292373.

%Y Cf. A289814 (analogous sequence for base-3).

%K nonn,base

%O 0,9

%A _Antti Karttunen_, Sep 15 2017