A101336 Alternating addition and subtraction of the residues of the primes less than the number.

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

Offset: 0

Author

Gordon Hamilton, Dec 24 2004

Keywords

• easy
• sign
• look

Comments

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).

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A024934.

Programs

Maple

a:= n-> add(-irem(n, ithprime(i))*(-1)^i, i=1..numtheory[pi](n)):
seq(a(n), n=0..100);  # Alois P. Heinz, Jul 27 2015

Mathematica

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 *)

Extensions

a(0)=0 prepended by Alois P. Heinz, Jul 27 2015