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

1,1

Links

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

Formula

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

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

Example

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

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)));

Prog

(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

Crossrefs

Cf. A001358, A046315, A100484.

Sequence in context: A248310 A133597 A075066 * A061363 A100077 A317739

Adjacent sequences: A384937 A384938 A384939 * A384941 A384942 A384943

Keyword

nonn,look

Author

Zak Seidov and Robert Israel, Jun 13 2025

Status

approved