OFFSET
0,1
LINKS
Robert Israel, Table of n, a(n) for n = 0..2500
EXAMPLE
2 + 3 = 5 (prime), 3 + 7 = 10 (semiprime), 7 + 11 = 18 (triprime).
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
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov, Oct 10 2022
STATUS
approved