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A024899 Numbers k such that 6*k + 1 is prime.

%I A024899 #59 Feb 04 2024 01:11:05
%S A024899 1,2,3,5,6,7,10,11,12,13,16,17,18,21,23,25,26,27,30,32,33,35,37,38,40,
%T A024899 45,46,47,51,52,55,56,58,61,62,63,66,68,70,72,73,76,77,81,83,87,90,91,
%U A024899 95,96,100,101,102,103,105,107,110,112,115,118,121,122,123,125,126,128,131,135,137
%N A024899 Numbers k such that 6*k + 1 is prime.
%C A024899 For all elements of this sequence there are no (x,y) positive integers such that a(n)=6*x*y+x+y or a(n)=6*x*y-x-y. - _Pedro Caceres_, Apr 19 2019
%H A024899 Ray Chandler, <a href="/A024899/b024899.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from T. D. Noe)
%F A024899 a(n) = A024892(n)/2 = (A034936(n)+1)/2. - _Ray Chandler_, Dec 26 2003
%F A024899 a(n) = (A002476(n)-1)/6. - _Zak Seidov_, Aug 31 2016
%p A024899 a := [ ]: for n from 0 to 400 do if isprime(6*n+1) then a := [ op(a), n ]; fi; od: A002476 := n->a[n];
%t A024899 Select[Range@ 140, PrimeQ[6 # + 1] &] (* _Michael De Vlieger_, Jan 23 2018 *)
%o A024899 (Magma) [n: n in [0..200]| IsPrime(6*n+1)] // _Vincenzo Librandi_, Nov 20 2010
%o A024899 (PARI) select(n->n%6==1,primes(100))\6 \\ _Charles R Greathouse IV_, Apr 28 2015
%Y A024899 A002476 gives primes, A091178 gives prime index.
%Y A024899 Complement of A046954 relative to A000027.
%K A024899 nonn,easy
%O A024899 1,2
%A A024899 _Clark Kimberling_