A336406 -id:A336406 - cp's OEIS frontend

A336407 a(n) is the number of composites < n-th odd composite.

3, 7, 11, 14, 16, 20, 22, 25, 29, 32, 34, 37, 39, 43, 45, 48, 52, 54, 57, 60, 62, 65, 67, 69, 72, 76, 80, 83, 85, 87, 89, 91, 93, 96, 99, 101, 105, 107, 109, 111, 115, 117, 120, 122, 125, 128, 130, 133, 135, 139, 141, 143, 145, 149, 153, 155, 157, 159, 161

Offset: 1

Clark Kimberling, Jul 20 2020

nonn

			a(2) is the number of the numbers 4, 6, 8, 9, 10, 12, 14, these being the composites that are less than 15, which is the 2nd odd composite.

Cf. A000040, A002808, A014076, A336406, A336408.

z = 400; p = Prime[Range[z]];
c = Select[Range[2, z], ! PrimeQ@# &];  (* A002808 *)
d = Select[Range[2, z], ! PrimeQ@# && OddQ@# &];  (* A014076 *)
f[n_] := Select[c, # < d[[n]] &];
g[n_] := d[[n]] + Select[c, # < d[[n]] &];
q[n_] := Length[Intersection[p, g[n]]];
tq = Table[q[n], {n, 1, 120}] (* A336406 *)
tc = Table[Length[f[n]], {n, 1, 120}] (* A336407 *)
m = Min[Length[tq], Length[tc]]; Take[tc, m] - Take[tq, m] (* A336408 *)

n=0;forcomposite(x=4,210,if(x%2,print1(n,", "));n++) \\ Hugo Pfoertner, Jul 26 2020

from sympy import primepi
def A336407(n):
    if n == 1: return 3
    m, k = n, (r:=primepi(n)) + n + (n>>1)
    while m != k:
        m, k = k, (r:=primepi(k)) + n + (k>>1)
    return m-r-2 # Chai Wah Wu, Jul 31 2024

A336408 a(n) = number of composites c+d such that c is a composite and d is the n-th odd composite.

Original entry on oeis.org

1, 4, 7, 8, 10, 13, 15, 17, 20, 22, 24, 24, 26, 31, 33, 35, 38, 40, 43, 44, 46, 47, 49, 52, 53, 58, 63, 63, 64, 66, 66, 68, 71, 73, 75, 77, 79, 80, 82, 84, 89, 91, 91, 94, 98, 99, 102, 103, 105, 109, 110, 111, 114, 117, 120, 122, 123, 125, 128, 129, 131, 131

Offset: 1

Clark Kimberling, Jul 20 2020

nonn

The n-th odd composite is A014076(n+1); the n-th composite is A002808(n).

			a(1) counts this sum: 6+9.
a(2) counts these sums: 6+15, 9+15, 10+15, 12+15.
a(3) counts these: 4+21, 6+21, 9+21, 12+21, 14+21, 15+21, 18+21.

Cf. A000040, A002808, A014076, A336406, A336407.

z = 400; p = Prime[Range[z]];
c = Select[Range[2, z], ! PrimeQ@# &];  (* A002808 *)
d = Select[Range[2, z], ! PrimeQ@# && OddQ@# &];  (* A014076 *)
f[n_] := Select[c, # < d[[n]] &];
g[n_] := d[[n]] + Select[c, # < d[[n]] &];
q[n_] := Length[Intersection[p, g[n]]];
tq = Table[q[n], {n, 1, 120}] (* A336406 *)
tc = Table[Length[f[n]], {n, 1, 120}] (* A336407 *)
m = Min[Length[tq], Length[tc]]; Take[tc, m] - Take[tq, m] (* A336408 *)

cp's OEIS Frontend

A336407 a(n) is the number of composites < n-th odd composite.

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