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A292370
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A binary encoding of the zeros in base-4 representation of n.
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5
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0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 3, 2, 2, 2, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 3, 2, 2, 2, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 3, 2, 2, 2, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 7, 6, 6, 6, 5, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4, 3, 2, 2, 2, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 3, 2, 2, 2, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 3, 2, 2, 2, 1, 0, 0, 0, 1
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OFFSET
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0,17
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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 0 2 0
3 0 3 0
4 1 10 1
5 0 11 0
6 0 12 0
7 0 13 0
8 1 20 1
9 0 21 0
10 0 22 0
11 0 23 0
12 1 30 1
13 0 31 0
14 0 32 0
15 0 33 0
16 3 100 11
17 2 101 10
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MATHEMATICA
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Table[FromDigits[IntegerDigits[n, 4] /. k_ /; IntegerQ@ k :> If[k == 0, 1, 0], 2], {n, 0, 120}] (* Michael De Vlieger, Sep 21 2017 *)
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PROG
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(Scheme) (define (A292370 n) (if (zero? n) n (let loop ((n n) (b 1) (s 0)) (if (< n 4) s (let ((d (modulo n 4))) (if (zero? d) (loop (/ n 4) (+ b b) (+ s b)) (loop (/ (- n d) 4) (+ b b) s)))))))
(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==0 else '0' for i in k), 2)
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CROSSREFS
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Cf. A291770 (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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