A165971 - OEIS

A165971

The n-th odd nonprime minus the n-th even nonprime.

1, 5, 9, 13, 15, 15, 19, 19, 21, 25, 27, 27, 29, 29, 33, 33, 35, 39, 39, 41, 43, 43, 45, 45, 45, 47, 51, 55, 57, 57, 57, 57, 57, 57, 59, 61, 61, 65, 65, 65, 65, 69, 69, 71, 71, 73, 75, 75, 77, 77, 81, 81, 81, 81, 85, 89, 89, 89, 89, 89, 91, 91, 91, 91, 91, 93, 97, 99, 99, 103

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000

FORMULA

a(n) = A014076(n) - A163300(n).

Equals: {1} U A160522.

EXAMPLE

a(1) = 1-0 = 1. a(2) = 9-4 = 5. a(3) = 15-6 = 9.

MATHEMATICA

A014076 := Select[Range@500, ! PrimeQ@# && OddQ@# &]; A163300 := Drop[Range[0, 500, 2], {2}]; Table[(-A163300[[n]] + A014076[[n]]), {n, 1, 50}] (* G. C. Greubel, Sep 17 2017 *)

PROG

(Python)

from sympy import primepi

def A165971(n):

if n == 1: return 1

m, k = n-1, primepi(n) + n - 1 + (n>>1)

while m != k:

m, k = k, primepi(k) + n - 1 + (k>>1)

return m-(n<<1) # Chai Wah Wu, Aug 01 2024

CROSSREFS

Cf. A014076, A163300, A141468, A160522.

Sequence in context: A080579 A325274 A303264 * A160522 A314651 A194371