

A071259


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


3



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
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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: A156624 A242932 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



