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A384940 Odd semiprimes interleaved with even semiprimes.

%I A384940 #13 Jun 18 2025 00:53:55
%S A384940 9,4,15,6,21,10,25,14,33,22,35,26,39,34,49,38,51,46,55,58,57,62,65,74,
%T A384940 69,82,77,86,85,94,87,106,91,118,93,122,95,134,111,142,115,146,119,
%U A384940 158,121,166,123,178,129,194,133,202,141,206,143,214,145,218,155,226,159,254,161,262,169,274,177
%N A384940 Odd semiprimes interleaved with even semiprimes.
%H A384940 Robert Israel, <a href="/A384940/b384940.txt">Table of n, a(n) for n = 1..10000</a>
%F A384940 a(2*k-1) = A046315(k).
%F A384940 a(2*k) = A100484(k).
%e A384940 a(3) = A046315(2) = 15 is the second odd semiprime.
%e A384940 a(4) = A100484(2) = 6 is the second even semiprime.
%p A384940 A:= select(t -> numtheory:-bigomega(t)=2, [seq(i,i=1..1000,2)]):
%p A384940 B:= select(t -> numtheory:-bigomega(t)=2, [seq(i,i=2..1000,2)]):
%p A384940 seq(op([A[i],B[i]]),i=1..min(nops(A),nops(B)));
%o A384940 (Python)
%o A384940 from math import isqrt
%o A384940 from sympy import primepi, primerange, prime
%o A384940 def A384940(n):
%o A384940     if n&1:
%o A384940         m = n+1>>1
%o A384940         def bisection(f,kmin=0,kmax=1):
%o A384940             while f(kmax) > kmax: kmax <<= 1
%o A384940             kmin = kmax >> 1		
%o A384940             while kmax-kmin > 1:
%o A384940                 kmid = kmax+kmin>>1
%o A384940                 if f(kmid) <= kmid:
%o A384940                     kmax = kmid
%o A384940                 else:
%o A384940                     kmin = kmid
%o A384940             return kmax
%o A384940         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)))
%o A384940         return bisection(f,m,m)
%o A384940     else:
%o A384940         return prime(n>>1)<<1 # _Chai Wah Wu_, Jun 17 2025
%Y A384940 Cf. A001358, A046315, A100484
%K A384940 nonn,look
%O A384940 1,1
%A A384940 _Zak Seidov_ and _Robert Israel_, Jun 13 2025