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URL: https://oeis.org/A129145

⇱ A129145 - OEIS

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A129145
Alternately odd prime and odd composite numbers.
2
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
1,1
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) <a(2n-1) (n-th odd prime larger than n-th odd composite number), cf. A129146
FORMULA
a(2n-1)=A065091(n), a(2n) =A071904(n).
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov, Apr 01 2007
STATUS
approved