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

0,8

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).

Links

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

Example

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

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 *)

Crossrefs

Cf. A024934.

Sequence in context: A213859 A330492 A350534 * A300001 A137218 A306765

Adjacent sequences: A101333 A101334 A101335 * A101337 A101338 A101339

Keyword

easy,sign,look

Author

Gordon Hamilton, Dec 24 2004

Extensions

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

Status

approved