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%I #12 Jun 30 2022 12:51:47
%S 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,
%T 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,
%U 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
%N A binary encoding of 3-digits in base-4 representation of n.
%H Antti Karttunen, <a href="/A292373/b292373.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) = A059905(A048735(n)) = A059906(A213370(n)).
%F For all n >= 0, A000120(a(n)) = A160383(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 0 2 0
%e 3 1 3 1
%e 4 0 10 0
%e 5 0 11 0
%e 6 0 12 0
%e 7 1 13 1
%e 8 0 20 0
%e 9 0 21 0
%e 10 0 22 0
%e 11 1 23 1
%e 12 2 30 10
%e 13 2 31 10
%e 14 2 32 10
%e 15 3 33 11
%e 16 0 100 0
%e 17 0 101 0
%e 18 0 102 0
%e 19 1 103 1
%o (Scheme, with memoization-macro definec)
%o (definec (A292373 n) (if (zero? n) n (let ((d (modulo n 4))) (+ (if (= 3 d) 1 0) (* 2 (A292373 (/ (- n d) 4)))))))
%o (Python)
%o def A292373(n): return int(bin(n&n>>1)[:1:-2][::-1],2) # _Chai Wah Wu_, Jun 30 2022
%Y Cf. A007088, A007090, A048735, A059905, A059906, A160383, A213370, A292370, A292371, A292372.
%K nonn,base
%O 0,13
%A _Antti Karttunen_, Sep 15 2017