A101336 - OEIS

%I #12 Jun 03 2017 17:25:22

%S 0,0,0,1,-1,-1,1,2,0,3,-4,-4,-2,-1,4,2,0,0,2,3,-4,6,-7,-7,-5,-9,3,7,

%T 13,14,10,10,9,2,-16,-13,-11,-10,7,23,16,16,25,26,13,11,-14,-14,-12,

%U -4,-10,-23,-11,-10,-9,-25,-20,2,29,29,26,27,-6,4,2,10,0,0,-18,-37,-36,-35,-34,-34,2,1,19,16,31,32,25,28,-15,-15,-6,-27,15

%N Alternating addition and subtraction of the residues of the primes less than the number.

%C The amplitude and periodicity of fluctuations increase... for example a(813) through a(836) are all positive and a(914) through a(937) all are positive except for a(922).

%H Alois P. Heinz, <a href="/A101336/b101336.txt">Table of n, a(n) for n = 0..10000</a>

%e a(10) = -4 because 10 (mod 2) - 10 (mod 3) + 10 (mod 5) - 10 (mod 7) = 0-1+0-3.

%p a:= n-> add(-irem(n, ithprime(i))*(-1)^i, i=1..numtheory[pi](n)):

%p seq(a(n), n=0..100);  # _Alois P. Heinz_, Jul 27 2015

%t Table[Total[Times@@@Partition[Riffle[Mod[n,Prime[Range[PrimePi[n]]]],{1,-1},{2,-1,2}],2]],{n,0,90}] (* _Harvey P. Dale_, Jun 03 2017 *)

%Y Cf. A024934.

%K easy,sign,look

%O 0,8

%A _Gordon Hamilton_, Dec 24 2004

%E a(0)=0 prepended by _Alois P. Heinz_, Jul 27 2015