A098449 - OEIS

%I #16 Apr 10 2021 10:34:53

%S 4,10,106,1003,10001,100001,1000001,10000001,100000001,1000000006,

%T 10000000003,100000000007,1000000000007,10000000000015,

%U 100000000000013,1000000000000003,10000000000000003,100000000000000015,1000000000000000007,10000000000000000001

%N Smallest n-digit semiprime.

%H Derek Orr, <a href="/A098449/b098449.txt">Table of n, a(n) for n = 1..60</a>

%t NextSemiPrime[n_, k_: 1] := Block[{c = 0, sgn = Sign[k]}, sp = n + sgn; While[c < Abs[k], While[ PrimeOmega[sp] != 2, If[sgn < 0, sp--, sp++]]; If[sgn < 0, sp--, sp++]; c++]; sp + If[sgn < 0, 1, -1]]; f[n_] := NextSemiPrime[10^n - 1]; Array[f, 19, 0] (* _Robert G. Wilson v_, Dec 18 2012 *)

%o (PARI)

%o a(n)=for(k=10^(n-1),10^n-1,if(bigomega(k)==2,return(k)))

%o vector(50, n, a(n)) \\ _Derek Orr_, Aug 15 2014

%o (Python)

%o from sympy import factorint

%o def semiprime(n): f = factorint(n); return sum(f[p] for p in f) == 2

%o def a(n):

%o   an = max(1, 10**(n-1))

%o   while not semiprime(an): an += 1

%o   return an

%o print([a(n) for n in range(1, 21)]) # _Michael S. Branicky_, Apr 10 2021

%Y Cf. A098450 (largest n-digit semiprime), A003617 (smallest n-digit prime), A001358 (semiprimes).

%K base,nonn

%O 1,1

%A _Rick L. Shepherd_, Sep 07 2004