A384940 Odd semiprimes interleaved with even semiprimes.

9, 4, 15, 6, 21, 10, 25, 14, 33, 22, 35, 26, 39, 34, 49, 38, 51, 46, 55, 58, 57, 62, 65, 74, 69, 82, 77, 86, 85, 94, 87, 106, 91, 118, 93, 122, 95, 134, 111, 142, 115, 146, 119, 158, 121, 166, 123, 178, 129, 194, 133, 202, 141, 206, 143, 214, 145, 218, 155, 226, 159, 254, 161, 262, 169, 274, 177

Offset: 1

Author

Zak Seidov and Robert Israel, Jun 13 2025

Keywords

• nonn
• look

Examples

			a(3) = A046315(2) = 15 is the second odd semiprime.
a(4) = A100484(2) = 6 is the second even semiprime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358, A046315, A100484

Programs

Maple

A:= select(t -> numtheory:-bigomega(t)=2, [seq(i,i=1..1000,2)]):
B:= select(t -> numtheory:-bigomega(t)=2, [seq(i,i=2..1000,2)]):
seq(op([A[i],B[i]]),i=1..min(nops(A),nops(B)));

Python

from math import isqrt
from sympy import primepi, primerange, prime
def A384940(n):
    if n&1:
        m = n+1>>1
        def bisection(f,kmin=0,kmax=1):
            while f(kmax) > kmax: kmax <<= 1
            kmin = kmax >> 1		
            while kmax-kmin > 1:
                kmid = kmax+kmin>>1
                if f(kmid) <= kmid:
                    kmax = kmid
                else:
                    kmin = kmid
            return kmax
        def f(x): return int(m+x+((t:=primepi(s:=isqrt(x)))*(t-1)>>1)-sum(primepi(x//k) for k in primerange(3, s+1)))
        return bisection(f,m,m)
    else:
        return prime(n>>1)<<1 # Chai Wah Wu, Jun 17 2025

Formula

a(2*k-1) = A046315(k).

a(2*k) = A100484(k).