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%I #7 Mar 30 2012 18:40:37
%S 1,8,42,174,705,2764,10772,41967,164793,654242,2634801,10787937,
%T 44983894,191249703,829651874,3673967785,16612478231,76708135651,
%U 361707435767,1741601413569,8561660600005
%N The 3-almost primeth recurrence: a(0) = 1, a(n+1) = 3-almostprime(a(n)) = A014612(a(n)).
%C 3-almostprime equivalent of Wilson's primeth recurrence: A007097.
%t ThreeAlmostPrimePi[n_] := Sum[PrimePi[n/(Prime@i*Prime@j)] - j + 1, {i, PrimePi[n^(1/3)]}, {j, i, PrimePi@Sqrt[n/Prime@i]}]; ThreeAlmostPrime[n_] := Block[{e = Floor[Log[2, n] + 1], a, b}, a = 2^e; Do[b = 2^p; While[ThreeAlmostPrimePi[a] < n, a = a + b]; a = a - b/2, {p, e, 0, -1}]; a + b/2]; NestList[ThreeAlmostPrime@# &, 1, 18]
%Y Cf. A007097, A105999, A119966.
%K nonn
%O 0,2
%A _Jonathan Vos Post_ and _Robert G. Wilson v_, May 31 2006
%E a(19)-a(20) from _Donovan Johnson_, Sep 29 2010
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