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Search: id:A133796
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| A133796 |
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a(n) = n-th prime + n-th semiprime. |
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+0
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
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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a(n) = A000040(n) + A001358(n).
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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.
SemiPrimePi[n_] := Sum[ PrimePi[n/Prime(AT)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 *)
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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 (mathar(AT)strw.leidenuniv.nl), Jan 07 2008
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CROSSREFS
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Cf. A000040, A001358.
Sequence in context: A002598 A036992 A047452 this_sequence A129413 A095098 A134859
Adjacent sequences: A133793 A133794 A133795 this_sequence A133797 A133798 A133799
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 05 2008
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EXTENSIONS
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Corrected and extended by Robert G. Wilson v (rgwv(AT)rgwv.com) and R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 05 2008
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