A098146 First odd semiprime > 10^n.

9, 15, 111, 1003, 10001, 100001, 1000001, 10000001, 100000001, 1000000013, 10000000003, 100000000007, 1000000000007, 10000000000015, 100000000000013, 1000000000000003, 10000000000000003, 100000000000000015

Offset: 0

Author

Hugo Pfoertner, Aug 28 2004

Keywords

• nonn

Examples

			a(0)=9 because 9=3*3 is the first odd semiprime following 10^0=1.
a(13) = 10000000000015 = 5*2000000000003.
		

Links

• Dario Alpern, Factorization using the Elliptic Curve Method.

Crossrefs

Cf. A046315 (odd semiprimes), A098147(n)=a(n)-10^n continuation of this sequence, A003717 (smallest n-digit prime).

Programs

Mathematica

osp[n_]:=Module[{k=1},While[PrimeOmega[n+k]!=2,k=k+2];n+k]; Join[{9}, Table[osp[10^i],{i,20}]] (* Harvey P. Dale, Jan 17 2012 *)

PARI

print1(9,","); for(n=1,10,forstep(i=10^n+1,10^(n+1)-1,2,f=factor(i); ms=matsize(f); if((ms[1]==1&&f[1,2]==2)||(ms[1]==2&&f[1,2]==1&&f[2,2]==1),print1(i,","); break))) /* Herman Jamke (hermanjamke(AT)fastmail.fm), Oct 21 2006 */

Python

from sympy import factorint, nextprime
def is_semiprime(n): return sum(e for e in factorint(n).values()) == 2
def next_odd_semiprime(n):
    nxt = n + 1 + n%2
    while not is_semiprime(nxt): nxt += 2
    return nxt
def a(n): return next_odd_semiprime(10**n)
print([a(n) for n in range(20)]) # Michael S. Branicky, Sep 15 2021