A073432 - OEIS

%I #13 Oct 15 2013 22:31:27

%S 1,4,8,12,15,17,21,23,26,30,33,35,38,40,44,46,49,53,55,58,61,63,66,68,

%T 70,73,77,81,84,86,88,90,92,94,97,100,102,106,108,110,112,116,118,121,

%U 123,126,129,131,134,136,140,142,144,146,150,154,156,158,160,162,165

%N Numbers n such that prime(n) + composite(n) is even.

%C For n > 1, numbers n such that the n-th composite number is odd. - _Charles R Greathouse IV_, Apr 03 2012

%H Charles R Greathouse IV, <a href="/A073432/b073432.txt">Table of n, a(n) for n = 1..10000</a>

%F Numbers n such that (A000040(n)+A002808(n))/2 is an integer.

%F a(n) ~ 2n since the primes have density 0. _Charles R Greathouse IV_, Apr 03 2012

%e 8 is in the sequence since prime(8)=19, composite(8)=15, and their average 17 is an integer.

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

%o (PARI) print1(n=1);for(c=6,1e3,if(isprime(c),next);n++;if(c%2,print1(", "n))) \\ _Charles R Greathouse IV_, Apr 03 2012

%Y Cf. A000040, A002808.

%K nonn,easy

%O 1,2

%A _Labos Elemer_, Jul 31 2002