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

1,1

Links

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

Formula

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

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A242932 A351863 A025201 * A231405 A092137 A206580

Adjacent sequences: A071256 A071257 A071258 * A071260 A071261 A071262

Keyword

nonn

Author

Amarnath Murthy, May 30 2002

Extensions

More terms from Labos Elemer, Jul 31 2002

Status

approved