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A179896 Sum of the numbers between k := n-th nonprime and 2k (like a jump in a Sieve of Eratosthenes). 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

LINKS

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

FORMULA

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

EXAMPLE

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

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 *)

CROSSREFS

Cf. A000040, A179545.

Sequence in context: A281917 A002798 A124388 * A075284 A057444 A130414

Adjacent sequences:  A179893 A179894 A179895 * A179897 A179898 A179899

KEYWORD

easy,nonn

AUTHOR

Odimar Fabeny, Jul 31 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

STATUS

approved

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Last modified June 24 11:11 EDT 2017. Contains 288697 sequences.