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%I #12 Feb 09 2017 03:03:47
%S 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,
%T 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,
%U 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
%N Parity of remainder Mod[p(n),n]=A004648(n).
%H Reinhard Zumkeller, <a href="/A072608/b072608.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n)=Mod[Mod[p(n), n], 2]=Mod[A004648(n), 2]
%e 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.
%t mm[x_] := Mod[Mod[Prime[x], x], 2] Table[mm[w], {w, 1, 256}]
%t Table[Mod[Mod[Prime[n],n],2],{n,110}] (* _Harvey P. Dale_, Apr 22 2016 *)
%o (Haskell
%o a072608 n = a000040 n `mod` n `mod` 2 -- _Reinhard Zumkeller_, Dec 16 2013
%o (PARI) a(n)=prime(n)%n%2 \\ _Charles R Greathouse IV_, Feb 09 2017
%Y Cf. A004648.
%K nice,nonn
%O 1,1
%A _Labos Elemer_, Jun 24 2002
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