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A225078 Numbers n such that n^2+1 and (n+1)^2-2 are both prime.

%I A225078 #15 Feb 16 2025 08:33:19
%S A225078 1,2,4,6,14,20,26,36,54,74,116,120,126,130,134,160,176,204,210,230,
%T A225078 236,256,264,284,300,314,340,386,420,440,466,490,496,544,594,636,644,
%U A225078 714,750,760,784,816,930,950,986,1070,1124,1140,1146,1156,1174,1176,1210
%N A225078 Numbers n such that n^2+1 and (n+1)^2-2 are both prime.
%C A225078 Prime limits of the Legendré conjecture for a given n.
%H A225078 Reinhard Zumkeller, <a href="/A225078/b225078.txt">Table of n, a(n) for n = 1..10000</a>
%H A225078 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LegendresConjecture.html">Legendre's Conjecture</a>
%H A225078 Wikipedia, <a href="http://en.wikipedia.org/wiki/Legendre%27s_conjecture">Legendre's conjecture</a>
%e A225078 n=2; n+1=3 ;n^2+1=5 and (n+1)^2-2=7.
%e A225078 n=490; n+1=491; n^2+1=240101 and (n+1)^2-2=241079.
%t A225078 Select[Range[2000], PrimeQ[#^2 + 1] && PrimeQ[(# + 1)^2 - 2] &] (* _T. D. Noe_, May 06 2013 *)
%o A225078 (TI-BASIC) ClrIO:Input "n",n:Lbl colorin:if isPrime(n^2+1) and
%o A225078 isPrime((n+1)^2-2) Then:Disp n:Pause:Endif:n+1(sto)n:Goto colorin:EndPrgm
%o A225078 (Haskell)
%o A225078 import Data.Function (on)
%o A225078 import Data.List (elemIndices)
%o A225078 a225078 n = a225078_list !! (n-1)
%o A225078 a225078_list = elemIndices 1 $
%o A225078    zipWith ((*) `on` a010051') a002522_list a008865_list
%o A225078 -- _Reinhard Zumkeller_, May 06 2013
%Y A225078 Cf. A002522, A008865, A010051, A014085, A002496, A028871.
%K A225078 nonn
%O A225078 1,2
%A A225078 _César Aguilera_, Apr 26 2013