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

%I A095277 #34 Sep 08 2022 08:45:13
%S A095277 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 A095277 46,48,50,51,53,54,57,58,60,61,63,64,66,68,69,71,72,73,74,75,78,79,80,
%U A095277 81,83,84,85,87,88,90,92,93,96,97,98,99,100,101,102,103,105,106,108
%N A095277 Numbers k such that 4k + 3 is composite.
%C A095277 Terms can be written as (4xy +- (x-y)) - 1 for x > 0, y > 0. - _Ron R Spencer_, Aug 01 2016
%C A095277 Numbers k such that (4*k)!/(4*k + 3) is an integer. - _Peter Bala_, Jan 25 2017
%H A095277 Vincenzo Librandi, <a href="/A095277/b095277.txt">Table of n, a(n) for n = 1..1000</a>
%F A095277 a(n) = (A091236(n) - 3)/4.
%e A095277 Distribution of the positive terms in the following triangular array:
%e A095277   *;
%e A095277   3,  *;
%e A095277   *,  8,  *;
%e A095277   6,  *, 15,  *;
%e A095277   *, 13,  *, 24,  *;
%e A095277   9,  *, 22,  *, 35,  *;
%e A095277   *, 18,  *, 33,  *, 48,  *;
%e A095277 etc., where * marks the noninteger values of (2*h*k + k + h-1)/2 with h >= k >= 1. - _Vincenzo Librandi_, Apr 22 2014
%p A095277 for n from 0 to 100 do
%p A095277 if irem(factorial(4*n), 4*n+3) = 0 then print(n); end if;
%p A095277 end do: # _Peter Bala_, Jan 25 2017
%t A095277 Select[Range[150],!PrimeQ[4#+3]&] (* _Harvey P. Dale_, Jul 04 2011 *)
%o A095277 (Magma) [n: n in [0..110] |not IsPrime(4*n+3)]; // _Vincenzo Librandi_, Apr 22 2014\
%o A095277 (PARI) is(n)=!isprime(4*n+3) \\ _Charles R Greathouse IV_, Aug 01 2016
%Y A095277 Complement of A095278. Cf. also A045751, A014076, A153170, A153088, A153329, A153343.
%K A095277 nonn,easy
%O A095277 1,1
%A A095277 _Antti Karttunen_, Jun 01 2004