cp's OEIS Frontend

A046954 Numbers k such that 6*k + 1 is nonprime.

%I A046954 #51 Sep 08 2022 08:44:56
%S A046954 0,4,8,9,14,15,19,20,22,24,28,29,31,34,36,39,41,42,43,44,48,49,50,53,
%T A046954 54,57,59,60,64,65,67,69,71,74,75,78,79,80,82,84,85,86,88,89,92,93,94,
%U A046954 97,98,99,104,106,108,109,111,113,114,116,117,119,120,124,127,129,130,132,133,134,136,139,140
%N A046954 Numbers k such that 6*k + 1 is nonprime.
%C A046954 Equals A171696 U A121763; A121765 U A171696 = A046953; A121763 U A121765 = A067611 where A067611 U A002822 U A171696 = A001477. - _Juri-Stepan Gerasimov_, Feb 13 2010, Feb 15 2010
%C A046954 These numbers (except 0) can be written as 6xy +-(x+y) for x > 0, y > 0. - _Ron R Spencer_, Aug 01 2016
%H A046954 Vincenzo Librandi, <a href="/A046954/b046954.txt">Table of n, a(n) for n = 1..1000</a>
%e A046954 a(2)=8 because 6*8 + 1 = 49, which is composite.
%p A046954 remove(k-> isprime(6*k+1), [$0..140])[]; # _Muniru A Asiru_, Feb 22 2019
%t A046954 a = Flatten[Table[If[PrimeQ[6*n + 1] == False, n, {}], {n, 0, 50}]] (* _Roger L. Bagula_, May 17 2007 *)
%t A046954 Select[Range[0, 200], !PrimeQ[6 # + 1] &] (* _Vincenzo Librandi_, Sep 27 2013 *)
%o A046954 (Haskell)
%o A046954 a046954 n = a046954_list !! (n-1)
%o A046954 a046954_list = map (`div` 6) $ filter ((== 0) . a010051' . (+ 1)) [0,6..]
%o A046954 -- _Reinhard Zumkeller_, Jul 13 2014
%o A046954 (PARI) is(n)=!isprime(6*n+1) \\ _Charles R Greathouse IV_, Aug 01 2016
%o A046954 (Magma) [n: n in [0..250] | not IsPrime(6*n+1)]; // _G. C. Greubel_, Feb 21 2019
%o A046954 (Sage) [n for n in (0..250) if not is_prime(6*n+1)] # _G. C. Greubel_, Feb 21 2019
%o A046954 (GAP) Filtered([0..250], k-> not IsPrime(6*k+1)) # _G. C. Greubel_, Feb 21 2019
%Y A046954 Cf. A047845 (2n+1), A045751 (4n+1), A127260 (8n+1).
%Y A046954 Cf. A046953, A008588, A016921, subsequence of A067611, complement of A024899.
%K A046954 nonn
%O A046954 1,2
%A A046954 _Felice Russo_
%E A046954 Edited by _N. J. A. Sloane_, Aug 08 2008 at the suggestion of _R. J. Mathar_
%E A046954 Corrected by _Juri-Stepan Gerasimov_, Feb 13 2010, Feb 15 2010
%E A046954 Corrected by _Vincenzo Librandi_, Sep 27 2013