A071259 Integer part of the arithmetic mean of the n-th prime p(n) and the n-th composite number C(n).

3, 4, 6, 8, 10, 12, 15, 17, 19, 23, 25, 29, 31, 33, 36, 39, 43, 44, 48, 51, 53, 56, 59, 62, 67, 70, 71, 74, 76, 79, 86, 89, 93, 94, 100, 101, 105, 109, 111, 115, 118, 120, 126, 128, 130, 132, 138, 145, 148, 149, 152, 156, 158, 163, 167, 170, 174, 176, 179, 182, 184

Offset: 1

Author

Amarnath Murthy, May 30 2002

Keywords

• nonn

Examples

			a(7) = {p(7) + C(7)}/2 = (17 + 14)/2 = 15.
p(9) = 23, C(9) = 16, average = 19.5, a(9) = 19.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..2500

Crossrefs

Cf. A000040, A002808, A073432, A073433, A071260.

Programs

Mathematica

c[x_] := FixedPoint[x+PrimePi[ # ]+1&, x] Do[s=(Prime[n]+c[n])/2; If[IntegerQ[s], Print[s]], {n, 1, 256}]
IntegerPart[Mean[#]]&/@Module[{nn=100,cmps},cmps=Select[Range[nn], CompositeQ]; Thread[{cmps,Prime[Range[Length[cmps]]]}]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Feb 24 2018 *)

Formula

Floor [ (p(n) + C(n))/2]

a(n)=Floor[[A000040(n)+A002808(n)]/2]; Prime[n]>a(n)>Composite[n]

Extensions

More terms from Labos Elemer, Jul 31 2002