A179464 a(n) = min(nextprime(n),nextsemiprime(n)).

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, 29, 29, 29, 31, 31, 33, 33, 34, 35, 37, 37, 38, 39, 41, 41, 43, 43, 46, 46, 46, 47, 49, 49, 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

Offset: 1

Author

Zak Seidov, Jan 08 2011

Keywords

• nonn

Examples

			n=1: nextprime(1)=2, nextsemiprime(1)=4, hence a(1)=2,
n=2: nextprime(2)=3, nextsemiprime(2)=4, hence a(2)=3,
n=3: nextprime(3)=5, nextsemiprime(3)=4, hence a(3)=4.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040 The prime numbers, A001358 Semiprimes.

Cf. A106325, A151800.

Programs

Maple

PS:= select(t -> numtheory:-bigomega(t)<=2, [$2..500]):
Res:= NULL:
k:= 1;
for n from 2 to max(PS) do
  if n > PS[k] then k:= k+1 fi;
  Res:= Res, PS[k];
od:
Res; # Robert Israel, Oct 25 2017

Mathematica

Table[m=n+1;While[2!= Plus@@Last/@FactorInteger[m],m++];Min[NextPrime[n],m],{n,200}]
mnp[n_]:=Module[{s=n+1},While[PrimeOmega[s]!=2,s++];Min[NextPrime[n],s]]; Array[mnp,100] (* Harvey P. Dale, Apr 23 2019 *)

PARI

{for(n=1,200,m=n+1;while(2<>bigomega(m),m++);print(min(nextprime(n+1),m)))}

Formula

a(n) = min(A106325(n+1), A151800(n)). - Robert Israel, Oct 25 2017