A174375 a(n) = n^2 - XOR(n^2, n).

0, 1, -2, -1, -4, -3, 2, -5, -8, -7, -10, 7, -12, 5, -6, -13, -16, -15, -18, -17, 12, 13, -14, 11, -24, 9, -26, 23, 4, -11, -22, -29, -32, -31, -34, -33, -36, -35, 34, 27, -40, -39, 22, 39, -44, 37, -38, 19, -48, 17, -50, 15, -20, 45, 18, -21, -56, 41, 6, -9, -28

Offset

0,3

Comments

Plotting the points of a(n) versus n up to a power of 2 approximates a Sierpinski gasket.

It follows from a(x + 2^k) = a(x) + 2^k (mod 2^(k+1)) that a is a bijection modulo 2^k for all k, as observed by Erling Ellingsen. Therefore, a is injective. Is it a bijection when considered as a function from Z to Z? - David Radcliffe, May 06 2023

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..8192

Fred Lunnon, Sketch of argument that sequence is a permutation of Z, SeqFan mailing list, May 30 2023.

Formula

a(n) = n^2 - XOR(n^2, n), where XOR is bitwise.

Mathematica

Table[n^2-BitXor[n^2, n], {n, 0, 60}] (* Harvey P. Dale, Jun 30 2011 *)

Prog

(Haskell)
a174375 n = n ^ 2 - a169810 n  -- Reinhard Zumkeller, Dec 27 2012
(PARI) a(n)=n^2 - bitxor(n^2, n) \\ Charles R Greathouse IV, Sep 27 2016
(Python) def a(n): return n * n - ((n * n) ^ n) # David Radcliffe, May 06 2023

Crossrefs

Cf. A169810.

Sequence in context: A205558 A082494 A194187 * A110663 A294317 A064277

Adjacent sequences: A174372 A174373 A174374 * A174376 A174377 A174378

Keyword

sign,nice,look

Author

Carl R. White, Mar 17 2010

Status

approved