|
%I #12 Apr 23 2019 15:49:04
%S 2,3,4,5,6,7,9,9,10,11,13,13,14,15,17,17,19,19,21,21,22,23,25,25,26,
%T 29,29,29,31,31,33,33,34,35,37,37,38,39,41,41,43,43,46,46,46,47,49,49,
%U 51,51,53,53,55,55,57,57,58,59,61,61,62,65,65,65,67,67,69,69,71,71,73,73,74,77,77,77,79,79,82,82,82,83,85,85,86,87,89,89,91,91,93,93,94
%N a(n) = min(nextprime(n),nextsemiprime(n)).
%H Robert Israel, <a href="/A179464/b179464.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = min(A106325(n+1), A151800(n)). - _Robert Israel_, Oct 25 2017
%e n=1: nextprime(1)=2, nextsemiprime(1)=4, hence a(1)=2,
%e n=2: nextprime(2)=3, nextsemiprime(2)=4, hence a(2)=3,
%e n=3: nextprime(3)=5, nextsemiprime(3)=4, hence a(3)=4.
%p PS:= select(t -> numtheory:-bigomega(t)<=2, [$2..500]):
%p Res:= NULL:
%p k:= 1;
%p for n from 2 to max(PS) do
%p if n > PS[k] then k:= k+1 fi;
%p Res:= Res, PS[k];
%p od:
%p Res; # _Robert Israel_, Oct 25 2017
%t Table[m=n+1;While[2!= Plus@@Last/@FactorInteger[m],m++];Min[NextPrime[n],m],{n,200}]
%t mnp[n_]:=Module[{s=n+1},While[PrimeOmega[s]!=2,s++];Min[NextPrime[n],s]]; Array[mnp,100] (* _Harvey P. Dale_, Apr 23 2019 *)
%o (PARI) {for(n=1,200,m=n+1;while(2<>bigomega(m),m++);print(min(nextprime(n+1),m)))}
%Y Cf. A000040 The prime numbers, A001358 Semiprimes.
%Y Cf. A106325, A151800.
%K nonn
%O 1,1
%A _Zak Seidov_, Jan 08 2011
|
