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A055755 4n^2+1, 2n^2+1, 2n^2-1 are all prime. 1

%I #8 Apr 02 2013 20:46:01

%S 3,42,45,102,132,153,237,297,375,468,570,990,2085,2478,2712,3240,4743,

%T 5382,5517,6828,7962,8970,8982,9033,9570,9612,9747,9813,10692,12363,

%U 12453,12468,12750,13902,14763,14925,15750,16365,17118,17688,19527

%N 4n^2+1, 2n^2+1, 2n^2-1 are all prime.

%H Peter J. C. Moses, <a href="/A055755/b055755.txt">Table of n, a(n) for n = 1..10000</a>

%e 42 is included because 4*42^2+1, 2*42^2+1, 2*42^2-1 are all prime numbers.

%p with(numtheory): for n from 1 to 50000 do if isprime(4*n^2+1) and isprime(2*n^2+1) and isprime(2*n^2-1) then printf(`%d,`,n) fi: od:

%t a={};Do[If[PrimeQ[4n^2+1] && PrimeQ[2n^2+1] && PrimeQ[2n^2-1], AppendTo[a,n]], {n,10000}]; a (* _Peter J. C. Moses_, Apr 02 2013 *)

%Y Cf. A001912.

%K easy,nonn

%O 1,1

%A _Harvey P. Dale_, Jul 12 2000

%E More terms from _James A. Sellers_, Jul 13 2000

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Last modified April 14 09:06 EDT 2024. Contains 371657 sequences. (Running on oeis4.)