A072608 Parity of remainder Mod(prime(n),n) = A004648(n).

0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0

Offset: 1

Author

Labos Elemer, Jun 24 2002

Keywords

• nice
• nonn
• easy

Examples

			n=25:p(25)=97,Mod[97,25]=22, a(25)=Mod[22,2]=0. With increasing n, a(n) alternates:...010101..,followed after by a range consisting only of 1-s. This secondary alternation also goes on.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A004648.

Programs

Haskell

a072608 n = a000040 n `mod` n `mod` 2 -- Reinhard Zumkeller, Dec 16 2013

Mathematica

mm[x_] := Mod[Mod[Prime[x], x], 2] Table[mm[w], {w, 1, 256}]
Table[Mod[Mod[Prime[n],n],2],{n,110}] (* Harvey P. Dale, Apr 22 2016 *)

PARI

a(n)=prime(n)%n%2 \\ Charles R Greathouse IV, Feb 09 2017

Formula

a(n) = Mod(Mod(prime(n), n), 2) = Mod(A004648(n), 2).