A073433 - OEIS

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A073433

Value of [p(n)+c(n)]/2 when it is integer; p(n) is n-th prime, c(n) is n-th composite.

3, 8, 17, 29, 36, 43, 53, 59, 70, 79, 93, 100, 109, 115, 128, 132, 148, 158, 167, 176, 184, 197, 204, 215, 222, 233, 247, 265, 274, 280, 288, 292, 301, 308, 319, 337, 346, 359, 368, 373, 380, 397, 401, 410, 419, 433, 448, 455, 466, 473, 496, 503, 507, 514

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..2000

FORMULA

[A000040(n)+A002808(n)]/2 when it is integer.

EXAMPLE

p(8)=19, c(8)=15, average=17, corresponds to 3rd term.

MATHEMATICA

c[x_] := FixedPoint[x+PrimePi[ # ]+1&, x] Do[s=(Prime[n]+c[n])/2; If[IntegerQ[s], Print[s]], {n, 1, 256}]

Module[{nn=200, pr, cm, len}, pr=Prime[Range[nn]]; cm=Select[Range[ nn], CompositeQ]; len=Min[Length[pr], Length[cm]]; Select[Total[#]/2&/@ Thread[ {Take[pr, len], Take[cm, len]}], IntegerQ]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 29 2019 *)

CROSSREFS

Cf. A000040, A002808, A073432.

Sequence in context: A048230 A294412 A227017 * A059518 A024929 A033816

Adjacent sequences: A073430 A073431 A073432 * A073434 A073435 A073436

KEYWORD

nonn

AUTHOR

Labos Elemer, Jul 31 2002

STATUS

approved