A189762 Greatest integer x such that x' = 2n+1, or 0 if there is no such x, where x' is the arithmetic derivative (A003415).

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

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

T. D. Noe, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A189759 A189760 A189761 * A189763 A189764 A189765

Keyword

nonn

Author

T. D. Noe, Apr 27 2011

Status

approved