A160522 The n-th odd composite number minus the n-th even composite number.

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, 103

Offset: 1

Author

Kyle Stern, May 16 2009

Keywords

• easy
• nonn

Links

• K. Stern, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A002808, A005843, A071904, A047846.

Programs

MATLAB

composite function [a] = A160522(k) j = 1; n = 1; even = 4; while j < k n = n + 1; if isprime(n) == 1 else if mod(n,2) == 0 else a(j,1) = n - even; even = even + 2; j = j + 1; end end end

Mathematica

Last[t = GatherBy[Select[Range[4, 245], ! PrimeQ[#] &], OddQ]] - Take[First[t], Length[Last[t]]] (* Jayanta Basu, Aug 11 2013 *)

PARI

m=70; v=vector(m); k=4; n=0; while(n0&&!isprime(k), n++; v[n]=k-2*(n+1)); k++); v \\ Klaus Brockhaus, May 22 2009

Python

from sympy import primepi
def A160522(n):
    if n == 1: return 5
    m, k = n, primepi(n) + n + (n>>1)
    while m != k:
        m, k = k, primepi(k) + n + (k>>1)
    return m-(n+1<<1) # Chai Wah Wu, Aug 01 2024

Formula

a(n) = A071904(n) - A005843(n+1).

Extensions

Extended and formula edited by Klaus Brockhaus, May 22 2009