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%I #23 Feb 18 2024 08:26:00
%S 290,550,850,1060,2650,3035,3245,5015,5105,8935,10615,11890,12925,
%T 13485,13905,14850,15215,15985,17560,17600,18105,19925,20135,21780,
%U 23510,24040,25490,28830,31145,34365,36355,38140,38370,42025,43845,46820,47575,48745,49130,50495,53350
%N Numbers k such that 6*k+1, 6*k+7, 6*k+13, 6*k+19 are consecutive primes.
%C All terms are == 0 (mod 5). - _Robert G. Wilson v_, Dec 12 2017
%H Robert Israel, <a href="/A090839/b090839.txt">Table of n, a(n) for n = 1..10000</a>
%e 6*290 + 1 = 1741, 6*290 + 7 = 1747, 6*290 + 13 = 1753, 6*290 + 19 = 1759 and 1741, 1747, 1753, 1759 are consecutive primes, so 290 is a term.
%t Block[{nn = 50500, s}, s = Select[Prime@ Range@ PrimePi[6 (nn + 3) - 1], Divisible[(# + 1), 6] &]; Select[Range@ nn, And[AllTrue[#, PrimeQ], Count[s, q_ /; First[#] < q < Last@ #] == 0] &@ Map[6 # + 1 &, # + Range[0, 3]] &]] (* _Michael De Vlieger_, Dec 06 2017 *)
%t fQ[n_] := Block[{p = {6n +1, 6n +7, 6n +13, 6n +19}}, Union@ PrimeQ@ p == {True} && NextPrime[6n +1, 3] == 6n +19]; Select[5 Range@ 10100, fQ] (* _Robert G. Wilson v_, Dec 12 2017 *)
%o (PARI) isok(n) = my(p,q,r); isprime(p=6*n+1) && ((q=6*n+7) == nextprime(p+1)) && ((r=6*n+13) == nextprime(q+1)) && (6*n+19 == nextprime(r+1)); \\ _Michel Marcus_, Sep 20 2019
%Y Cf. A033451, A090832, A090833, A090834, A090835, A090836, A090837, A090838.
%K easy,nonn
%O 1,1
%A _Pierre CAMI_, Dec 09 2003
%E Missing term 5105 and more terms from _Michel Marcus_, Sep 20 2019
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