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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)):
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
KEYWORD
easy,sign,look
AUTHOR
Gordon Hamilton, Dec 24 2004
EXTENSIONS
a(0)=0 prepended by Alois P. Heinz, Jul 27 2015
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)