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A133796
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a(n) = n-th prime + n-th semiprime.
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1
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6, 9, 14, 17, 25, 28, 38, 41, 48, 55, 64, 71, 76, 81, 86, 99, 108, 112, 122, 128, 131, 141, 148, 158, 171, 178, 185, 192, 195, 200, 218, 224, 231, 234, 255, 262, 272, 281, 286, 294, 301, 304, 320, 326, 331, 340, 353, 366, 372, 375, 388, 397, 400, 412, 423, 432
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OFFSET
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1,1
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LINKS
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FORMULA
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EXAMPLE
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a(1) = 1st prime + 1st semiprime = 2 + 4 = 6.
a(2) = 2nd prime + 2nd semiprime = 3 + 6 = 9.
a(3) = 3rd prime + 3rd semiprime = 5 + 9 = 14.
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MAPLE
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A000040 := proc(n) ithprime(n) ; end: A001358 := proc(n) option remember ; local a ; if n = 1 then 4 ; else for a from A001358(n-1)+1 do if numtheory[bigomega](a) = 2 then RETURN(a) ; fi ; od: fi ; end: A133796 := proc(n) A000040(n)+A001358(n) ; end: seq(A133796(n), n=1..100) ; # R. J. Mathar, Jan 07 2008
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MATHEMATICA
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SemiPrimePi[n_] := Sum[ PrimePi[n/Prime@i] - i + 1, {i, PrimePi@ Sqrt@n}]; SemiPrime[n_] := Block[{e = Floor[Log[2, n] + 1], a, b}, a = 2^e; Do[b = 2^p; While[SemiPrimePi@a < n, a = a + b]; a = a - b/2, {p, e, 0, -1}]; a + b/2]; f[n_] := Prime@n + SemiPrime@n; Array[f, 56] (* Robert G. Wilson v *)
Module[{nn=300, pr, semi, len}, pr=Prime[Range[PrimePi[nn]]]; semi=Select[ Range[ nn], PrimeOmega[#]==2&]; len=Min[Length[pr], Length[semi]]; Total/@ Thread[{Take[pr, len], Take[semi, len]}]] (* Harvey P. Dale, Jun 27 2014 *)
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PROG
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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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