A118909 a(1) = 4; a(n) is least semiprime > a(n-1)^2.

4, 21, 445, 198026, 39214296677, 1537761063871773242347, 2364709089560047865452947255794201194068433, 5591849078247910476736920566826713466552016538943524658263883555662554776622687075541

Offset: 1

Author

Jonathan Vos Post, May 05 2006

Keywords

• easy
• nonn

Comments

Semiprime analog of A055496 a(1) = 2; a(n) is smallest prime > 2*a(n-1). See also A059785 a(n+1)=prevprime(a(n)^2), with a(1) = 2. With that, of course, there's always a prime between n and 2n, so a(n) < 2^n. The obverse of this is A118908 a(1) = 4; a(n) is greatest semiprime < a(n-1)^2.

Examples

			a(8) = a(7)^2 + 52 and there is no smaller k such that a(7)^2 + k is semiprime.
		

Crossrefs

Cf. A001358, A055496, A076656, A006992, A005384, A005385, A118908-A118913.

Programs

Mathematica

nxt[n_]:=Module[{sp=n^2+1},While[PrimeOmega[sp]!=2,sp++];sp]; NestList[nxt,4,7] (* Harvey P. Dale, Oct 22 2012 *)

Python

from itertools import accumulate
from sympy.ntheory.factor_ import primeomega
def nextsemiprime(n):
  while primeomega(n + 1) != 2: n += 1
  return n + 1
def f(anm1, _): return nextsemiprime(anm1**2)
print(list(accumulate([4]*6, f))) # Michael S. Branicky, Apr 21 2021