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A179896
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Sum of the numbers between k := n-th nonprime and 2k (like a jump in a Sieve of Eratosthenes).
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4
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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FORMULA
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EXAMPLE
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0(0) = 0, 1(2) = 0, 4(8) = 5,6,7 = 18, 6(12) = 7,8,9,10,11 = 45 and so on.
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MAPLE
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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:
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MATHEMATICA
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f[n_] := Plus @@ Range[n + 1, 2 n - 1]; f /@ Select[ Range@ 64, ! PrimeQ@# &] (* Robert G. Wilson v, Sep 02 2010 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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