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A095277 Numbers k such that 4k + 3 is composite. 9

%I

%S 3,6,8,9,12,13,15,18,21,22,23,24,27,28,29,30,33,35,36,38,39,42,43,45,

%T 46,48,50,51,53,54,57,58,60,61,63,64,66,68,69,71,72,73,74,75,78,79,80,

%U 81,83,84,85,87,88,90,92,93,96,97,98,99,100,101,102,103,105,106,108

%N Numbers k such that 4k + 3 is composite.

%C Terms can be written as (4xy +- (x-y)) - 1 for x > 0, y > 0. - _Ron R Spencer_, Aug 01 2016

%C Numbers k such that (4*k)!/(4*k + 3) is an integer. - _Peter Bala_, Jan 25 2017

%H Vincenzo Librandi, <a href="/A095277/b095277.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = (A091236(n) - 3)/4.

%e Distribution of the positive terms in the following triangular array:

%e *;

%e 3, *;

%e *, 8, *;

%e 6, *, 15, *;

%e *, 13, *, 24, *;

%e 9, *, 22, *, 35, *;

%e *, 18, *, 33, *, 48, *;

%e etc., where * marks the noninteger values of (2*h*k + k + h-1)/2 with h >= k >= 1. - _Vincenzo Librandi_, Apr 22 2014

%p for n from 0 to 100 do

%p if irem(factorial(4*n), 4*n+3) = 0 then print(n); end if;

%p end do: # _Peter Bala_, Jan 25 2017

%t Select[Range[150],!PrimeQ[4#+3]&] (* _Harvey P. Dale_, Jul 04 2011 *)

%o (MAGMA) [n: n in [0..110] |not IsPrime(4*n+3)]; // _Vincenzo Librandi_, Apr 22 2014\

%o (PARI) is(n)=!isprime(4*n+3) \\ _Charles R Greathouse IV_, Aug 01 2016

%Y Complement of A095278. Cf. also A045751, A014076, A153170, A153088, A153329, A153343.

%K nonn,easy

%O 1,1

%A _Antti Karttunen_, Jun 01 2004

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Last modified April 7 13:17 EDT 2020. Contains 333305 sequences. (Running on oeis4.)