A129145 Alternately odd prime and odd composite numbers.

3, 9, 5, 15, 7, 21, 11, 25, 13, 27, 17, 33, 19, 35, 23, 39, 29, 45, 31, 49, 37, 51, 41, 55, 43, 57, 47, 63, 53, 65, 59, 69, 61, 75, 67, 77, 71, 81, 73, 85, 79, 87, 83, 91, 89, 93, 97, 95, 101, 99, 103, 105, 107, 111, 109, 115, 113, 117, 127, 119, 131, 121, 137, 123, 139, 125

Offset: 1

Author

Zak Seidov, Apr 01 2007

Keywords

• nonn

Comments

For small n's a(2n) >a(2n-1) (that is for small n's, n-th odd prime less than n-th odd composite number), while for large n's a(2n) A129146

Crossrefs

Cf. A065091, A071904, A129131, A129146.

Programs

Mathematica

Module[{nn=100,pr,cm,len},pr=Prime[Range[2,nn+1]];cm=Select[Range[ 9,2nn+1,2],CompositeQ];len=Min[Length[pr],Length[cm]];Riffle[Take[ pr,len],Take[cm,len]]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 10 2019 *)

Python

from sympy import prime, primepi
def A129145(n):
    if n&1: return prime((n>>1)+2)
    if n==2: return 9
    r = n>>1
    m, k = r, primepi(r) + r + (r>>1)
    while m != k:
        m, k = k, primepi(k) + r + (k>>1)
    return m # Chai Wah Wu, Aug 01 2024

Formula

a(2n-1)=A065091(n), a(2n) =A071904(n).