A118909 - OEIS

A118909

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

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

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OFFSET

1,1

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.

LINKS

Table of n, a(n) for n=1..8.

EXAMPLE

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

MATHEMATICA

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

PROG

(Python)

from itertools import accumulate

from sympy.ntheory.factor_ import primeomega

def nextsemiprime(n):

while primeomega(n + 1) != 2: n += 1