A357713 a(0) = 2; afterwards a(n) is the least prime greater than a(n-1) such that Omega(a(n-1) + a(n)) = n.

2, 3, 7, 11, 13, 19, 197, 251, 389, 1531, 2053, 3067, 17669, 25339, 66821, 105211, 140549, 318203, 1008901, 1940219, 6710533, 9804539, 12215557, 34970363, 49964293, 75864827, 276456709, 864393979, 1350198533, 2877659899, 4101661957, 7709498107, 16449692933, 51196041979

Offset: 0

Author

Zak Seidov, Oct 10 2022

Keywords

• nonn

Examples

			2 + 3 = 5 (prime), 3 + 7 = 10 (semiprime), 7 + 11 = 18 (triprime).
		

Links

• Robert Israel, Table of n, a(n) for n = 0..2500

Crossrefs

Cf. A001222 (Omega).

Programs

Maple

f:= proc(n, a) # first prime b>a such that a+b is an n-almost-prime
  uses priqueue;
  local Aprimes, v, M, q, w;
  M:= 10^100;
  initialize(Aprimes);
  insert([-2^n, 0, 2], Aprimes);
  do
    v:= extract(Aprimes);
    if v[2] = n then
      if -v[1] > 2*a and isprime(-v[1]-a) then return -v[1]-a fi
    else
      insert(v+[0, 1, 0], Aprimes);
      q:= nextprime(v[3]);
      w:= v[1]*(q/v[3])^(n-v[2]);
      if w >= -M then insert([w, v[2], q], Aprimes) fi
    fi
  od
end proc:
R:= 2: a:= 2:
for n from 1 to 30 do
  a:= f(n,a);
  R:= R,a;
od:
R; # Robert Israel, Sep 19 2023

Mathematica

s = {p = 2}; Do[q = NextPrime[p]; While[k != PrimeOmega[p + q], q = NextPrime[q]]; AppendTo[s, p = q], {k, 30}]; s