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A330270
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a(n) is the least nonnegative integer k such that n XOR k is a square (where XOR denotes the bitwise XOR operator).
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4
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0, 0, 2, 2, 0, 1, 2, 3, 1, 0, 3, 2, 5, 4, 7, 6, 0, 1, 2, 3, 4, 5, 6, 7, 1, 0, 3, 2, 5, 4, 7, 6, 4, 5, 6, 7, 0, 1, 2, 3, 12, 13, 14, 15, 8, 9, 10, 11, 1, 0, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12, 15, 14, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1
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OFFSET
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0,3
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COMMENTS
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This sequence has similarities with A329794 as the XOR operator and the "box" operator defined in A329794 both map (n, n) to 0 for any n (however here we accept 0 as a square).
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LINKS
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FORMULA
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a(n) = 0 iff n is a square.
a(a(n)) <= n.
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EXAMPLE
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For n = 7,
- 7 XOR 0 = 7 (not a square),
- 7 XOR 1 = 6 (not a square),
- 7 XOR 2 = 5 (not a square),
- 7 XOR 3 = 4 = 2^2,
- hence a(7) = 3.
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MATHEMATICA
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A330270[n_] := Module[{k = -1}, While[!IntegerQ[Sqrt[BitXor[n, ++k]]]]; k];
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PROG
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(PARI) a(n) = for (k=0, oo, if (issquare(bitxor(n, k)), return (k)))
(Python)
from itertools import count
from sympy.ntheory.primetest import is_square
def A330270(n): return next(k for k in count(0) if is_square(n^k)) # Chai Wah Wu, Aug 22 2023
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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