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A292372
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A binary encoding of 2-digits in base-4 representation of n.
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6
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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)
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OFFSET
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0,9
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LINKS
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FORMULA
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EXAMPLE
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n a(n) base-4(n) binary(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
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MATHEMATICA
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Table[FromDigits[IntegerDigits[n, 4] /. k_ /; IntegerQ@ k :> If[k == 2, 1, 0], 2], {n, 0, 120}] (* Michael De Vlieger, Sep 21 2017 *)
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PROG
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(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)
(Python)
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
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CROSSREFS
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Cf. A289814 (analogous sequence for base-3).
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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