A105999 Semiprimeth recurrence: a(0) = 1, a(n+1) = semiprime(a(n)) = A001358(a(n)).

1, 4, 10, 26, 77, 235, 779, 2785, 10643, 43697, 192893, 915218, 4657929, 25380749, 147721169, 916036271, 6037442989, 42191467826, 311911160465, 2434014941905, 20007995450483, 172911791611798, 1568190042677867

Offset: 0

Author

Jonathan Vos Post, Apr 29 2005

Keywords

• nonn

Comments

Semiprime equivalent of R. G. Wilson's primeth recurrence: A007097.

Examples

			a(1) = A001358(1) = 4,
a(2) = A001358(a(1)) = A001358(4) = 10,
a(3) = A001358(a(2)) = A001358(10) = 26.
		

Crossrefs

Cf. A001358, A007097, A091022, A105997, A105998.

Programs

Mathematica

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]; NestList[SemiPrime@# &, 1, 18] (* Robert G. Wilson v, May 31 2006 *)

Extensions

a(5)-a(15) from Robert G. Wilson v, Apr 30 2005

a(16)-a(20) from Robert G. Wilson v, May 31 2006

a(21)-a(22) from Donovan Johnson, Sep 24 2010