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

Offset: 1

Author

Juri-Stepan Gerasimov, Oct 02 2009

Keywords

• nonn
• less

Examples

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

Links

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

Crossrefs

Cf. A014076, A163300, A141468, A160522.

Programs

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 *)

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

Formula

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

Equals: {1} U A160522.

Extensions

77 duplicated by R. J. Mathar, Oct 10 2009