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

0,3

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

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 *)

Prog

(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 */
(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
(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

Crossrefs

Sequence in context: A262437 A130909 A275993 * A002377 A053836 A025483

Adjacent sequences: A160697 A160698 A160699 * A160701 A160702 A160703

Keyword

nonn,easy

Author

Reinhard Zumkeller, Jun 01 2009

Status

approved