A100351 Numbers n such that n-2^k is a semiprime for all k > 0 with 2^k < n.

8, 4311

Offset: 1

Author

T. D. Noe, Nov 18 2004

Keywords

• bref
• more
• nonn

Comments

A subset of A100349. No others < 10^9; conjecture that this sequence is finite.

Next term, if it exists, exceeds 5*10^10. [From Sean A. Irvine, Apr 13 2010]

Examples

			4311-2=31*139, 4311-4=59*73, 4311-8=13*331, 4311-16=5*859, 4311-32=11*389, 4311-64=31*137, 4311-128=47*89, 4311-256=5*811, 4311-512=29*131, 4311-1024=19*173, 4311-2048=31*73, 4311-4096=5*43
		

Crossrefs

Cf. A039669 (n such that n-2^k is prime), A100349 (n such that n-2^k is prime or semiprime), A100350 (primes p such that p-2^k is prime or semiprime).

Programs

Mathematica

SemiPrimeQ[n_Integer] := If[Abs[n]<2, False, (2==Plus@@Transpose[FactorInteger[Abs[n]]][[2]])]; lst={}; Do[k=1; While[p=n-2^k; p>0 && SemiPrimeQ[p], k++ ]; If[p<=0, AppendTo[lst, n]], {n, 3, 1000000}]; lst