A179896 Sum of the numbers between k := n-th nonprime and 2k (like a jump in a Sieve of Eratosthenes).

0, 18, 45, 84, 108, 135, 198, 273, 315, 360, 459, 570, 630, 693, 828, 900, 975, 1053, 1134, 1305, 1488, 1584, 1683, 1785, 1890, 2109, 2223, 2340, 2583, 2838, 2970, 3105, 3384, 3528, 3675, 3825, 3978, 4293, 4455, 4620, 4788, 4959, 5310, 5673, 5859, 6048, 6240, 6435

Offset: 1

Author

Odimar Fabeny, Jul 31 2010

Keywords

• easy
• nonn

Comments

The values 4, 7, 10... (A016777 for n>1) are the values of floor( a(k)/ A018252(k) ) where k runs through the indices where A179879(k) mod A018252(k) != 0. - Odimar Fabeny.

Proof: a(k)/A018252(k) is 3*(A081252(k)-1)/2. This is a non-integer iff A018252(k) is even. Since the n-th even nonprime is 2*n+2, floor(3*(2*n+1)/2) = 3*n+1=a(n). - Robert Israel, Aug 27 2014

Examples

			0(0) = 0, 1(2) = 0, 4(8) = 5,6,7 = 18, 6(12) = 7,8,9,10,11 = 45 and so on.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A179545.

Programs

Maple

ithnonprime := proc(n)local k: option remember: if(n=1)then return 1: else k := procname(n-1)+1: while true do if(not isprime(k))then return k fi: k:=k+1: od: fi: end:
A179896 := proc(n)local k: k:=ithnonprime(n): return 3*k*(k-1)/2: end:
seq(A179896(n),n=1..40); # Nathaniel Johnston, Apr 21 2011

Mathematica

f[n_] := Plus @@ Range[n + 1, 2 n - 1]; f /@ Select[ Range@ 64, ! PrimeQ@# &] (* Robert G. Wilson v, Sep 02 2010 *)

Formula

a(n) = A045943(A141468(n+1)-1). - R. J. Mathar, Sep 01 2010

Extensions

More terms from Odimar Fabeny, Aug 11 2010

Offset adapted to A141468 and to match another 0 - R. J. Mathar, Sep 01 2010