A114125 a(n) is the 10^n-th semiprime.

4, 26, 314, 3595, 40882, 459577, 5109839, 56168169, 611720495, 6609454805, 70937808071, 757060825018, 8040423200947, 85037651263063, 896113850117314, 9413000361625346, 98597629032410971, 1030179406403917981, 10739422018595513973, 111729397883168684917, 1160260967837159869621

Offset

0,1

Links

Table of n, a(n) for n=0..20.

Eric Weisstein's World of Mathematics, Semiprime.

Formula

a(n) = A001358(10^n). - Chai Wah Wu, Jun 04 2026

Mathematica

fQ[n_] := Plus @@ Last /@ FactorInteger@n == 2; c = 0; k = 2; Do[While[c < 10^n, If[fQ@k, c++ ]; k++ ]; Print[k - 1], {n, 0, 8}]
(* checked by *) SemiPrimePi[n_] := Sum[ PrimePi[n/Prime@i] - i + 1, {i, PrimePi@ Sqrt@n}]

Prog

(Perl) use ntheory ":all"; print "$_ ", nth_semiprime(10**$_), "\n" for 0..15; # Dana Jacobsen, Oct 08 2018
(Python)
from math import isqrt
from sympy import primepi, primerange
from oeis_sequences.OEISsequences import bisection
def A114125(n):
    n10 = 10**n
    def f(x): return int(n10+x+((t:=primepi(s:=isqrt(x)))*(t-1)>>1)-sum(primepi(x//p) for p in primerange(s+1)))
    return bisection(f, n10, n10) # Chai Wah Wu, Jun 04 2026

Crossrefs

Cf. A001358, A006880, A006988, A066265, A078972.

Sequence in context: A271613 A271614 A136503 * A063182 A293954 A348117

Adjacent sequences: A114122 A114123 A114124 * A114126 A114127 A114128

Keyword

nonn

Author

Robert G. Wilson v, Feb 11 2006

Extensions

a(14) from Donovan Johnson, Sep 27 2010

Corrected a(14), added a(15)-a(18) from Dana Jacobsen, Oct 10 2018

a(19)-a(20) from Henri Lifchitz, Nov 08 2024

Status

approved