A073432 Numbers n such that prime(n) + composite(n) is even.

1, 4, 8, 12, 15, 17, 21, 23, 26, 30, 33, 35, 38, 40, 44, 46, 49, 53, 55, 58, 61, 63, 66, 68, 70, 73, 77, 81, 84, 86, 88, 90, 92, 94, 97, 100, 102, 106, 108, 110, 112, 116, 118, 121, 123, 126, 129, 131, 134, 136, 140, 142, 144, 146, 150, 154, 156, 158, 160, 162, 165

Offset: 1

Author

Labos Elemer, Jul 31 2002

Keywords

• nonn
• easy

Comments

For n > 1, numbers n such that the n-th composite number is odd. - Charles R Greathouse IV, Apr 03 2012

Examples

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

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A002808.

Programs

Mathematica

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

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

Formula

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

a(n) ~ 2n since the primes have density 0. Charles R Greathouse IV, Apr 03 2012