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%I #20 Sep 08 2022 08:45:21
%S 4,60,180,760,910,1020,1230,1600,1860,2160,2280,2440,3850,5800,7320,
%T 8680,12940,13780,14740,17350,17400,21840,22720,22960,26040,27010,
%U 31050,33870,34060,35200,39900,40030,44350,45280,45540,45750,50460,52050
%N Numbers k such that 1*k + 1, 3*k + 1, 9*k + 1, 27*k + 1 are all primes.
%C Conjecture: all terms except the first are multiples of 10. - _Harvey P. Dale_, Mar 26 2015
%H Harvey P. Dale, <a href="/A112041/b112041.txt">Table of n, a(n) for n = 1..1000</a>
%e 1*4 + 1 = 5;
%e 3*4 + 1 = 13;
%e 9*4 + 1 = 37;
%e 27*4 + 1 = 109; 5, 13, 37, 109 are all prime so 4 is in the sequence.
%t Select[Range[60000],AllTrue[3^Range[0,3]*#+1,PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Mar 26 2015 *)
%o (Magma) [n: n in [1..100000] |IsPrime(n+1) and IsPrime(3*n+1) and IsPrime(9*n+1) and IsPrime(27*n+1)] // _Vincenzo Librandi_, Nov 13 2010
%Y Cf. A112042, A112043.
%K nonn
%O 1,1
%A _Pierre CAMI_, Aug 26 2005
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