A109403 Examine the sequence of all (even or odd) semiprimes, A001358, and record the averages of any pair of successive terms of the same parity.

5, 12, 18, 50, 53, 56, 60, 67, 89, 92, 113, 120, 126, 131, 144, 160, 173, 184, 186, 204, 211, 216, 220, 236, 242, 248, 251, 266, 276, 288, 290, 293, 300, 304, 307, 320, 322, 328, 337, 340, 368, 374, 379, 384, 392

Offset: 1

Author

Zak Seidov, Jun 27 2005

Keywords

• nonn

Examples

			5 is OK because sp(1)=4, sp(2)=6 and (4+6)/2=5; 12 is OK because sp(4)=10, sp(5)=14 and (10+14)/2=12; sp(n)=n-th semiprime.
		

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A001358, A100484.

Programs

Maple

A001358 := proc(n) option remember; local a; if n = 1 then 4; else for a from procname(n-1)+1 do if numtheory[bigomega](a) = 2 then return a; end if; end do: end if; end proc:
# To produce a b-file
M:=50000; c:=0;
for n from 1 to M do
if type(A001358(n)+A001358(n+1),even) then c:=c+1;
m:=(A001358(n)+A001358(n+1))/2;
lprint(c,m);
fi; od; # N. J. A. Sloane, Aug 27 2020

Mathematica

 Select[Mean/@Partition[Select[Range[400],PrimeOmega[#]==2&],2,1],IntegerQ] (* Harvey P. Dale, Aug 27 2020 *)

Extensions

Definition corrected by N. J. A. Sloane, Aug 26 2020. The original definition appeared to be based on A100484, but that was incorrect. Thanks to Harvey P. Dale for pointing out that something was wrong.