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%I #53 Sep 08 2022 08:44:56
%S 6,11,13,16,20,21,24,26,27,31,34,35,36,37,41,46,48,50,51,54,55,56,57,
%T 61,62,63,66,68,69,71,73,76,79,81,83,86,88,89,90,91,92,96,97,101,102,
%U 104,105,106,111,112,115,116,118,119,121,122,123,125,126,128
%N Numbers k such that 6*k - 1 is composite.
%C These numbers can be written as 6*x*y + x - y for x > 0, y > 0. - _Ron R Spencer_, Aug 01 2016
%H Reinhard Zumkeller, <a href="/A046953/b046953.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) ~ n. - _Charles R Greathouse IV_, Aug 01 2016
%e a(1)=6 because 6*6 - 1 = 35, which is composite.
%p remove(k-> isprime(6*k-1), [$1..130])[]; # _Muniru A Asiru_, Feb 22 2019
%t Select[Range[200],!PrimeQ[6#-1]&] (* _Vladimir Joseph Stephan Orlovsky_, Feb 25 2011 *)
%o (Haskell)
%o a046953 n = a046953_list !! (n-1)
%o a046953_list = map (`div` 6) $
%o filter ((== 0) . a010051' . subtract 1) [6,12..]
%o -- _Reinhard Zumkeller_, Jul 13 2014
%o (PARI) is(n)=!isprime(6*n-1) \\ _Charles R Greathouse IV_, Aug 01 2016
%o (Magma) [n: n in [1..200] | not IsPrime(6*n-1)]; // _G. C. Greubel_, Feb 21 2019
%o (Sage) [n for n in (1..200) if not is_prime(6*n-1)] # _G. C. Greubel_, Feb 21 2019
%o (GAP) Filtered([1..200], k-> not IsPrime(6*k-1)) # _G. C. Greubel_, Feb 21 2019
%Y Cf. A046954, A008588, A016969, subsequence of A067611.
%Y Cf. A024898 (complement).
%K nonn
%O 1,1
%A _Felice Russo_
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