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Alternately odd prime and odd composite numbers.
2

%I #10 Aug 01 2024 14:59:46

%S 3,9,5,15,7,21,11,25,13,27,17,33,19,35,23,39,29,45,31,49,37,51,41,55,

%T 43,57,47,63,53,65,59,69,61,75,67,77,71,81,73,85,79,87,83,91,89,93,97,

%U 95,101,99,103,105,107,111,109,115,113,117,127,119,131,121,137,123,139,125

%N Alternately odd prime and odd composite numbers.

%C 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

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

%t 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 *)

%o (Python)

%o from sympy import prime, primepi

%o def A129145(n):

%o if n&1: return prime((n>>1)+2)

%o if n==2: return 9

%o r = n>>1

%o m, k = r, primepi(r) + r + (r>>1)

%o while m != k:

%o m, k = k, primepi(k) + r + (k>>1)

%o return m # _Chai Wah Wu_, Aug 01 2024

%Y Cf. A065091, A071904, A129131, A129146.

%K nonn

%O 1,1

%A _Zak Seidov_, Apr 01 2007