A160700 a(n) = if n<16 then n else a(floor(n/16)) XOR (n mod 16).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1, 0, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12, 15, 14, 2, 3, 0, 1, 6, 7, 4, 5, 10, 11, 8, 9, 14, 15, 12, 13, 3, 2, 1, 0, 7, 6, 5, 4, 11, 10, 9, 8, 15, 14, 13, 12, 4, 5, 6, 7, 0, 1, 2, 3, 12, 13, 14, 15, 8, 9, 10, 11, 5, 4, 7, 6, 1, 0, 3, 2, 13

Offset: 0

Author

Reinhard Zumkeller, Jun 01 2009

Keywords

• nonn
• easy

Comments

A very simple hash function for the nonnegative integers.

a(A000079(n))=A133145(n); a(A000302(n))=A010685(n); a(A001025(n))=A161452(n); a(A161440(n))=0; a(A161441(n))=1; a(A161442(n))=2; a(A161443(n))=3; a(A161444(n))=4; a(A161445(n))=5; a(A161446(n))=6; a(A161447(n))=7; a(A161448(n))=8; a(A161449(n))=9; a(A161450(n))=10; a(A161451(n))=11; a(A161452(n))=12; a(A161453(n))=13; a(A161454(n))=14; a(A161455(n))=15. - Reinhard Zumkeller, Jun 10 2009

Links

• R. Zumkeller, Table of n, a(n) for n = 0..10000

Programs

Haskell

import Data.Bits (xor)
a160700 n = a160700_list !! n
a160700_list = [0..15] ++ map f [16..] where
   f x = a160700 x' `xor` m :: Int where (x', m) = divMod x 16
-- Reinhard Zumkeller, Nov 07 2012

Maple

read("transforms") ;
A160700 := proc(n)
    if n < 16 then
        n;
    else
        XORnos(procname(floor(n/16)),modp(n,16))
    end if;
end proc: # R. J. Mathar, Jul 12 2016

Mathematica

a[n_] := a[n] = If[n < 16, n, a[Floor[n/16]] ~BitXor~ Mod[n, 16]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Jan 25 2018 *)

Maxima

load(functs)$
A160700(n):=if n<16 then n else logxor(floor(n/16),mod(n,16))$
makelist(A160700(n),n,0,60); /* Martin Ettl, Nov 05 2012 */

PARI

a(n)=my(t=n%16); while(n>15, n>>=4; t=bitxor(t, n%16)); t \\ Charles R Greathouse IV, Jan 25 2018