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A336407
a(n) is the number of composites < n-th odd composite.
3
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
1,1
EXAMPLE
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.
MATHEMATICA
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 *)
PROG
(PARI) n=0; forcomposite(x=4, 210, if(x%2, print1(n, ", ")); n++) \\ Hugo Pfoertner, Jul 26 2020
(Python)
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
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jul 20 2020
STATUS
approved