

A330270


a(n) is the least nonnegative integer k such that n XOR k is a square (where XOR denotes the bitwise XOR operator).


4



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

0,3


COMMENTS

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).


LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..8192
Rémy Sigrist, Scatterplot of the ordinal transform of the first 2^20 terms
Rémy Sigrist, Scatterplot of (x, y) such that x XOR y is a square, 0 <= x, y <= 1023


FORMULA

a(n) = 0 iff n is a square.
a(a(n)) <= n.


EXAMPLE

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.


PROG

(PARI) a(n) = for (k=0, oo, if (issquare(bitxor(n, k)), return (k)))


CROSSREFS

See A330271 for the cube variant.
Cf. A000290, A003987, A295520, A329794.
Sequence in context: A101565 A292944 A327188 * A029341 A240181 A079070
Adjacent sequences: A330267 A330268 A330269 * A330271 A330272 A330273


KEYWORD

nonn,base,easy


AUTHOR

Rémy Sigrist, Dec 08 2019


STATUS

approved



