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Numbers k such that 2*k + 3 is composite.
18

%I #39 Sep 08 2022 08:45:39

%S 3,6,9,11,12,15,16,18,21,23,24,26,27,30,31,33,36,37,39,41,42,44,45,46,

%T 48,51,54,56,57,58,59,60,61,63,65,66,69,70,71,72,75,76,78,79,81,83,84,

%U 86,87,90,91,92,93,96,99,100,101,102,103,105,106,107,108,109,111,114

%N Numbers k such that 2*k + 3 is composite.

%C One less than the associated value in A047845. - _R. J. Mathar_, Jan 05 2011

%H Vincenzo Librandi, <a href="/A153238/b153238.txt">Table of n, a(n) for n = 1..10000</a>

%H Marc Wolf, François Wolf, <a href="https://hal.archives-ouvertes.fr/hal-01832624 ">Representation theorem of composite odd numbers indices</a>, SCIREA Journal of Mathematics (2018) 3.3, 106-117.

%F a(n) ~ n. - _Charles R Greathouse IV_, Dec 28 2011

%t lst={};Do[If[ !PrimeQ[2*n+3],AppendTo[lst,n]],{n,6!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jan 10 2009 *)

%t Select[Range[120], CompositeQ[2 # + 3] &] (* _Michael De Vlieger_, Oct 17 2018 *)

%o (PARI) for(n=1,115,if(!isprime(2*n+3),print1(n,", "))) \\ _Joerg Arndt_, Dec 19 2010

%o (Magma) [ n: n in [0..120] | not IsPrime(2*n+3) ]; // _Klaus Brockhaus_, Dec 19 2010

%Y Cf. A067076, A047845, A144562.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Dec 21 2008

%E Edited by _Ray Chandler_, Jan 07 2009