%I #9 Jul 08 2023 10:41:35
%S 1,7,25,873,1375,41875,903123,1015623,49671873,200921875,1157734375,
%T 41898828123,496308203125,10506958984375,7739037109375,
%U 382999267578123,17016876976778523,46804302197265625,80713609326109375
%N a(n) is the least odd number k such that Omega(k) = n and Omega(k+2) = n+1, where Omega(k) is the number of prime factors of k (A001222).
%e a(3) = 873 because Omega(873) = Omega(3^2*97) = 3, Omega(873+2) = Omega(5^3*7) = 4 and 873 is the smallest such integer.
%t a[n_] := Block[{ov=0, v=1, k=3}, While[ov != n || v != n+1, ov = v; k += 2; v = PrimeOmega@ k]; k-2]; a /@ Range[0, 6]
%o (PARI)
%o generate(A, B, n, k) = A=max(A, 2^n); (f(m, p, n) = my(list=List()); if(n==1, forprime(q=max(p,ceil(A/m)), B\m, my(t=m*q); if(bigomega(t-2) == k, listput(list, t-2))), forprime(q=p, sqrtnint(B\m, n), list=concat(list, f(m*q, q, n-1)))); list); vecsort(Vec(f(1, 3, n)));
%o a(n) = my(x=2^n, y=2*x); while(1, my(v=generate(x, y, n+1, n)); if(#v >= 1, return(v[1])); x=y+1; y=2*x); \\ _Daniel Suteu_, Jul 08 2023
%Y Cf. A001222, A322300, A335496.
%K nonn,more
%O 0,2
%A _Giovanni Resta_, Jun 11 2020
%E a(12)-a(18) from _Daniel Suteu_, Jul 08 2023