|
|
A101336
|
|
Alternating addition and subtraction of the residues of the primes less than the number.
|
|
2
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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)):
|
|
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
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|