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Numbers n such that n, 2n+1, 3n+2, 4n+3 are primes.
9

%I #21 Sep 08 2022 08:45:05

%S 5,89,1409,1889,10589,11549,11909,12899,17159,19889,22349,24239,26189,

%T 35999,37049,37379,39419,44879,45569,49919,60779,67559,68669,75329,

%U 83579,88919,104369,108359,112349,114599,127139,133979,135029,135449

%N Numbers n such that n, 2n+1, 3n+2, 4n+3 are primes.

%C Terms are congruent to {5,29} mod 30. - _Zak Seidov_, May 31 2012

%H Zak Seidov, <a href="/A067257/b067257.txt">Table of n, a(n) for n = 1..1000</a>

%t Select[Prime[Range[10^5]],PrimeQ[2*#+1]&&PrimeQ[3*#+2]&&PrimeQ[4*#+3] &] (* _Vladimir Joseph Stephan Orlovsky_, Apr 27 2008 *)

%o (Magma) [n: n in [1..150000] | IsPrime(n) and IsPrime(2*n+1) and IsPrime(3*n+2) and IsPrime(4*n+3)]; // _Vincenzo Librandi_, Oct 31 2014

%Y Cf. A000040, A005384, A067256, A067258, A101767-A101770.

%K nonn

%O 1,1

%A _Benoit Cloitre_, Feb 20 2002

%E Extended by _Ray Chandler_, Dec 31 2004