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A255218 Numbers k such that 12*k+1, 24*k+1, 36*k+1 and 72*k+1 are all prime.

%I A255218 #31 Dec 20 2024 17:43:51
%S A255218 28,103,190,253,355,848,1328,1783,1898,1958,1988,2170,2213,3003,3533,
%T A255218 3808,3913,3988,4450,4488,4593,4800,5460,5808,5853,6448,6545,6903,
%U A255218 7103,7238,7295,7400,7483,7693,8533,9310,9780,10260,10885,12185,12628,15513,16163
%N A255218 Numbers k such that 12*k+1, 24*k+1, 36*k+1 and 72*k+1 are all prime.
%H A255218 Amiram Eldar, <a href="/A255218/b255218.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)
%H A255218 Umberto Cerruti, <a href="/A255218/a255218.pdf">Pseudoprimi di Fermat e numeri di Carmichael</a> (in Italian), p. 14.
%t A255218 Select[Range[10000], PrimeQ[12 # + 1] && PrimeQ[24 # + 1] && PrimeQ[36 # + 1] && PrimeQ[72 # + 1] &]
%t A255218 Select[Range[17000],AllTrue[{12,24,36,72}#+1,PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, May 16 2016 *)
%o A255218 (Magma) [n: n in [0..20000] | IsPrime(12*n+1) and IsPrime(24*n+1) and IsPrime(36*n+1) and IsPrime(72*n+1)];
%o A255218 (Magma) [n: n in [0..20000] | forall{i: i in Divisors(6) | IsPrime(12*i*n+1)}];
%Y A255218 Subsequence of A110801 and A111174.
%Y A255218 Cf. A255578.
%K A255218 nonn
%O A255218 1,1
%A A255218 _Vincenzo Librandi_, Feb 26 2015