A189657 Start with n, apply k->2k+1 until a semiprime is reached; sequence gives the semiprimes.

15, 95, 15, 9, 95, 55, 15, 35, 39, 21, 95, 25, 55, 119, 511, 33, 35, 303, 39, 335, 87, 91, 95, 49, 51, 215, 55, 57, 119, 123, 511, 65, 543, 69, 143, 295, 303, 77, 159, 327, 335, 85, 87, 5759, 91, 93, 95, 391, 799, 203, 415, 54271, 215, 219, 111, 3647, 115

Offset: 0

Author

Jonathan Vos Post, Apr 25 2011

Keywords

• nonn
• easy

Comments

This is to semiprimes A001358 as A051919 is to primes A000040. Is this sequence defined for all n?

Examples

			a(0) = 15 in 4 steps because 2*(2*(2*((2*0)+1)+1)+1)+1 = 15 = 3*5 is semiprime.
a(1) = 15 in 3 steps because 2*(2*((2*1) + 1)+1)+1 = 15 = 3*5
a(2) = 95 in 5 steps because 2*(2*(2*(2*(2*2 + 1)+1)+1)+1)+1 = 95 = 5*19.
		

Crossrefs

Cf. A001358, A051919.

Programs

Mathematica

semiPrimeQ[n_] := Total[FactorInteger[n]][[2]]==2; Table[k = n; While[k = 2 k + 1; ! semiPrimeQ[k]]; k, {n, 100}] (* T. D. Noe, Apr 29 2011 *)

Extensions

Extended by T. D. Noe, Apr 29 2011