|
%I #23 Jun 11 2023 14:22:27
%S 0,2,4,66,1012,14630,929390,63798350
%N a(n) is the first number k such that k + a(i) has n prime factors, counted with multiplicity, for all i < n; a(0) = 0.
%C a(8) > 3*10^9 if it exists.
%F A001222(a(i) + a(j)) = j for 0 <= i < j.
%e a(3) = 66 because a(0) + 66 = 66 = 2*3*11, a(1) + 66 = 68 = 2*2*17, and a(2) + 66 = 70 = 2*5*7 all have 3 prime factors, counted with multiplicity, and 66 is the least number that works.
%p A:= [0]:
%p for i from 1 to 7 do
%p for x from 2^i do if andmap(t -> numtheory:-bigomega(t+x) = i, A) then
%p A:= [op(A), x]; break
%p fi od od:
%p A;
%Y Cf. A001222.
%K nonn,more
%O 0,2
%A _Robert Israel_, Mar 21 2023
|
