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%I #17 Aug 30 2014 06:06:57
%S 0,18,45,84,108,135,198,273,315,360,459,570,630,693,828,900,975,1053,
%T 1134,1305,1488,1584,1683,1785,1890,2109,2223,2340,2583,2838,2970,
%U 3105,3384,3528,3675,3825,3978,4293,4455,4620,4788,4959,5310,5673,5859,6048,6240,6435
%N Sum of the numbers between k := n-th nonprime and 2k (like a jump in a Sieve of Eratosthenes).
%C 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_.
%C 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
%H Nathaniel Johnston, <a href="/A179896/b179896.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A045943(A141468(n+1)-1). - _R. J. Mathar_, Sep 01 2010
%e 0(0) = 0, 1(2) = 0, 4(8) = 5,6,7 = 18, 6(12) = 7,8,9,10,11 = 45 and so on.
%p 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:
%p A179896 := proc(n)local k: k:=ithnonprime(n): return 3*k*(k-1)/2: end:
%p seq(A179896(n),n=1..40); # _Nathaniel Johnston_, Apr 21 2011
%t f[n_] := Plus @@ Range[n + 1, 2 n - 1]; f /@ Select[ Range@ 64, ! PrimeQ@# &] (* _Robert G. Wilson v_, Sep 02 2010 *)
%Y Cf. A000040, A179545.
%K easy,nonn
%O 1,2
%A _Odimar Fabeny_, Jul 31 2010
%E More terms from _Odimar Fabeny_, Aug 11 2010
%E Offset adapted to A141468 and to match another 0 - _R. J. Mathar_, Sep 01 2010
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