A336409 Distance from prime(n) to the nearest odd composite that is < prime(n).

2, 4, 2, 4, 2, 2, 4, 2, 2, 4, 2, 2, 2, 4, 2, 2, 4, 2, 2, 2, 2, 2, 4, 2, 4, 2, 2, 2, 2, 4, 2, 4, 2, 2, 2, 2, 2, 4, 2, 4, 2, 4, 2, 2, 2, 4, 2, 2, 4, 2, 2, 2, 2, 4, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 4, 2, 2, 2, 2, 2, 4

Offset: 5

Author

Clark Kimberling, Sep 06 2020

Keywords

• nonn

Examples

			Beginning with prime(5) = 11:  11-9 = 2, 13-9 = 4, 17-15 = 2, 19-15 = 4.
		

Crossrefs

Cf. A175191, A014076, A336410, A336411, A062301.

Programs

Maple

A336409 := proc(n)
    local p;
    p := ithprime(n) ;
    for a from p-2 by -2 do
        if not isprime(a) then
            return p-a ;
        end if;
    end do:
end proc:
seq(A336409(n),n=5..100) ; # R. J. Mathar, Oct 02 2020
# second Maple program:
a:= n-> `if`(isprime(ithprime(n)-2), 4, 2):
seq(a(n), n=5..100);  # Alois P. Heinz, Oct 02 2020

Mathematica

z = 5000; d = Select[Range[2, z], ! PrimeQ@# && OddQ@# &];  (* A014076 *)
f[n_] := Select[d, # < Prime[n] &];
t = Table[Prime[n] - Max[f[n]], {n, 5, 300}]  (* A336409 *)
Flatten[Position[t, 2]]  (* A336410 *)
Flatten[Position[t, 4]]  (* A336411 *)

Formula

a(n) = 2 * A175191(n-1). - Alois P. Heinz, Oct 02 2020

a(n) = 2 * (A062301(n) + 1). - Hugo Pfoertner, Oct 02 2020