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A178084 Numbers k for which 10k + 1, 10k + 3, 10k + 7, 10k + 9 and 10k + 13 are primes.

%I A178084 #15 Sep 08 2022 08:45:53
%S A178084 1,10,148,1606,1942,2101,2227,4378,5533,14416,16570,16684,19573,20182,
%T A178084 22534,24760,26881,32614,34798,36121,39775,46516,51880,53644,63346,
%U A178084 63379,66109,76819,79579,82972,85795,87601,95854,100885,102250,106396
%N A178084 Numbers k for which 10k + 1, 10k + 3, 10k + 7, 10k + 9 and 10k + 13 are primes.
%C A178084 These primes sets are just like 3k-4 and 3k-2 (or 6k-1 and 6*k+1) prime pairs, only five in a row.
%H A178084 Aaron Toponce, <a href="/A178084/b178084.txt">Table of n, a(n) for n = 1..1000</a>
%e A178084 k =    1:    11,    13,    17,    19,    23,
%e A178084 k =   10:   101,   103,   107,   109,   113,
%e A178084 k =  148:  1481,  1483,  1487,  1489,  1493,
%e A178084 k = 1606: 16061, 16063, 16067, 16069, 16073,
%e A178084 k = 1942: 19421, 19423, 19427, 19429, 19433,
%e A178084 k = 2101: 21011, 21013, 21017, 21019, 21023,
%e A178084 k = 2227: 22271, 22273, 22277, 22279, 22283
%t A178084 Flatten[Table[If[PrimeQ[10* n + 1] && PrimeQ[10*n + 3] && PrimeQ[10*n + 7] && PrimeQ[10*n + 9] && PrimeQ[10*(n + 1) + 3], n, {}], {n, 0, 50000}]]
%o A178084 (Magma) [n: n in [0..1000]| IsPrime(10*n+1) and IsPrime(10*n+3) and IsPrime(10*n+7) and IsPrime(10*n+9) and IsPrime(10*n+13)] // _Vincenzo Librandi_, Nov 30 2010
%Y A178084 Cf. A007811.
%K A178084 nonn
%O A178084 1,2
%A A178084 _Roger L. Bagula_, May 19 2010
%E A178084 More terms from _Vincenzo Librandi_, May 23 2010