A165955 - OEIS

%I #13 Aug 02 2024 02:01:31

%S 1,13,21,29,35,39,47,51,57,65,71,75,81,85,93,97,103,111,115,121,127,

%T 131,137,141,145,151,159,167,173,177,181,185,189,193,199,205,209,217,

%U 221,225,229,237,241,247,251,257,263,267,273,277,285,289,293,297,305,313,317,321,325

%N n-th odd nonprime plus n-th even nonprime.

%H G. C. Greubel, <a href="/A165955/b165955.txt">Table of n, a(n) for n = 1..5000</a>

%F a(n) = A014076(n) + A163300(n).

%e a(1) = 1+0 = 1. a(2) = 9+4 = 13. a(3) = 15+6 = 21.

%t 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 *)

%t Module[{nn=300,np,enp,onp,len},np=Select[Range[0,nn],!PrimeQ[#]&];enp= Select[ np,EvenQ];onp=Select[np,OddQ];len=Min[Length[enp], Length[ onp]]; Total/@Thread[{Take[enp,len],Take[onp,len]}]] (* _Harvey P. Dale_, Nov 28 2018 *)

%o (Python)

%o from sympy import primepi

%o def A165955(n):

%o     if n == 1: return 1

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

%o     while m != k:

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

%o     return m+(n<<1) # _Chai Wah Wu_, Aug 01 2024

%Y Cf. A014076, A141468, A163300.

%K nonn

%O 1,2

%A _Juri-Stepan Gerasimov_, Oct 01 2009

%E Entries checked by _R. J. Mathar_, Oct 10 2009