A336410 -id:A336410 - cp's OEIS frontend

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

Clark Kimberling, Sep 06 2020

nonn

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

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

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

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 *)

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

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

A336411 a(n) = A029707(n+2) - 3 for n >= 1.

Original entry on oeis.org

2, 4, 7, 10, 14, 17, 23, 25, 30, 32, 38, 40, 42, 46, 49, 54, 57, 61, 66, 78, 80, 86, 95, 101, 106, 110, 113, 117, 137, 139, 141, 145, 149, 168, 170, 173, 175, 179, 187, 198, 203, 206, 209, 212, 222, 227, 231, 233, 250, 253, 259, 262, 265, 274, 283, 285, 291

Offset: 1

Clark Kimberling, Sep 06 2020

nonn

Previous name was "Numbers k such that prime(k) - oc(k) = 4, where oc(k) is the greatest odd composite < prime(k)".

Complement of A336410.

Cf. A000040, A014076, A029707, A107770, A155752, A336409.

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]]  (* this sequence *)

a(n) = A029707(n+2) - 3 = A155752(n+2) - 2. - Hugo Pfoertner, Oct 02 2020

Offset corrected by Mohammed Yaseen, Jul 17 2023

New name from Hugo Pfoertner, Jul 19 2023

cp's OEIS Frontend

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

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