OFFSET
1,2
COMMENTS
Indices n such that the (n+1)st semiprime has a prime factor which is the next prime after one of the prime factors of the n-th semiprime. - R. J. Mathar, Apr 20 2010
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
EXAMPLE
a(1)=1 because semiprime(1)/prime(1)=2 and semiprime(2)/prime(2)=2;
a(2)=2 because semiprime(2)/prime(1)=3 and semiprime(3)/prime(2)=3;
a(3)=3 because semiprime(3)/prime(2)=3 and semiprime(4)/prime(3)=2.
MAPLE
From R. J. Mathar, Apr 20 2010: (Start)
isA001358 := proc(n) numtheory[bigomega](n) = 2 ; end proc:
A001358 := proc(n) option remember ; if n = 1 then return 4 ; else for a from procname(n-1)+1 do if isA001358(a) then return a; end if; end do; end if; end proc:
A176486 := proc(n) if n = 1 then 1; else for a from procname(n-1)+1 do spl := A084126(a) ; sph := A084127(a) ; sp2l := A084126(a+1) ; sp2h := A084127(a+1) ; if sp2l = nextprime(spl) or sp2h = nextprime(spl) or sp2l = nextprime(sph) or sp2h = nextprime(sph) then return a; end if; end do: end if; end proc:
seq(A176486(n), n=1..80) ; (End)
MATHEMATICA
sppQ[{a_, b_}]:=Module[{t=NextPrime[Transpose[FactorInteger[a]][[1]]], c, d}, c=t[[1]]; d=If[Length[t]>1, t[[2]], t[[1]]]; Divisible[b, c]|| Divisible[ b, d]]; Flatten[ Position[Partition[Select[Range[1500], PrimeOmega[#] == 2&], 2, 1], _?sppQ]] (* Harvey P. Dale, Mar 16 2015 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Juri-Stepan Gerasimov, Apr 18 2010
EXTENSIONS
Corrected (59, 137, 142 inserted, 147 removed) and extended by R. J. Mathar, Apr 20 2010
STATUS
approved