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A189762 Greatest integer x such that x' = 2n+1, or 0 if there is no such x, where x' is the arithmetic derivative (A003415). 4
0, 6, 10, 14, 0, 22, 26, 0, 34, 38, 0, 46, 27, 0, 58, 62, 0, 0, 74, 42, 82, 86, 0, 94, 63, 0, 106, 0, 70, 118, 122, 0, 0, 134, 105, 142, 146, 98, 0, 158, 0, 166, 117, 0, 178, 0, 175, 0, 194, 130, 202, 206, 0, 214, 218, 154, 226, 0, 245, 138, 171, 0, 0, 254 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Bisection of A099303. In contrast to the sequence for even numbers, A102084, there appear to be an infinite number of zeros in this sequence (see A098700). The density of the zeros appears to be 1/3. Quite Often a(n) = 4n-2. For odd number 2n+1, an upper bound on the largest anti-derivative x appears to ((2n+1)/3)^(3/2).
LINKS
MATHEMATICA
dn[0] = 0; dn[1] = 0; dn[n_] := Module[{f = Transpose[FactorInteger[n]]}, If[PrimeQ[n], 1, Plus @@ (n*f[[2]]/f[[1]])]]; nn = 100; d = Array[dn, (nn/2)^2]; Table[pos = Position[d, n]; If[pos == {}, 0, pos[[-1, 1]]], {n, 3, nn, 2}]
CROSSREFS
Cf. A003415, A099303, A102084 (another bisection of A099303).
Sequence in context: A315157 A135596 A233456 * A163814 A088706 A087710
KEYWORD
nonn
AUTHOR
T. D. Noe, Apr 27 2011
STATUS
approved

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)