A119965 The 3-almost primeth recurrence: a(0) = 1, a(n+1) = 3-almostprime(a(n)) = A014612(a(n)).

1, 8, 42, 174, 705, 2764, 10772, 41967, 164793, 654242, 2634801, 10787937, 44983894, 191249703, 829651874, 3673967785, 16612478231, 76708135651, 361707435767, 1741601413569, 8561660600005

Offset: 0

Author

Jonathan Vos Post and Robert G. Wilson v, May 31 2006

Keywords

• nonn

Comments

3-almostprime equivalent of Wilson's primeth recurrence: A007097.

Crossrefs

Cf. A007097, A105999, A119966.

Programs

Mathematica

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]

Extensions

a(19)-a(20) from Donovan Johnson, Sep 29 2010