A098450 - OEIS

%I #17 Sep 18 2021 07:17:05

%S 9,95,998,9998,99998,999997,9999998,99999997,999999991,9999999997,

%T 99999999997,999999999997,9999999999989,99999999999997,

%U 999999999999998,9999999999999994,99999999999999989,999999999999999993,9999999999999999991,99999999999999999983

%N Largest n-digit semiprime.

%H Amiram Eldar, <a href="/A098450/b098450.txt">Table of n, a(n) for n = 1..100</a>

%F a(n) = 10^n - A119320(n). - _Amiram Eldar_, Sep 18 2021

%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, 18] (* _Robert G. Wilson v_, Dec 18 2012 *)

%o (PARI) apply( A098450(n)={n=10^n;until(bigomega(n-=1)==2,);n}, [1..20]) \\ _M. F. Hasler_, Jan 01 2021

%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 = 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. A098449 (smallest n-digit semiprime), A003618 (largest n-digit prime), A001358 (semiprimes), A119320.

%K base,nonn

%O 1,1

%A _Rick L. Shepherd_, Sep 07 2004