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

Author

Carl R. White, Mar 17 2010

Keywords

• sign
• nice
• look

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.

Crossrefs

Cf. A169810.

Programs

Haskell

a174375 n = n ^ 2 - a169810 n  -- Reinhard Zumkeller, Dec 27 2012

Mathematica

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

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

Formula

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