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Primes of the form (n+1)^3 - n^2.
2

%I #13 Sep 08 2022 08:45:40

%S 7,23,109,191,307,463,919,1231,1607,2053,4657,7639,8861,34913,41719,

%T 53503,77743,89189,95311,122599,138007,146173,182057,223381,246203,

%U 353011,383833,416399,433351,468623,505759,544807,721079,745471,875711

%N Primes of the form (n+1)^3 - n^2.

%H G. C. Greubel, <a href="/A154113/b154113.txt">Table of n, a(n) for n = 1..2000</a>

%e 2^3-1^2=7, 3^3-2^2=23, ...

%t a[n_]:=(n+1)^3-n^2;lst={};Do[If[PrimeQ[a[n]],AppendTo[lst,a[n]]],{n,6!}];lst

%t Select[(#+1)^3-#^2&/@Range[200],PrimeQ] (* _Harvey P. Dale_, Mar 14 2011 *)

%o (Magma) [a: n in [0..100] | IsPrime(a) where a is (n+1)^3 - n^2]; // _Vincenzo Librandi_, Sep 02 2016

%o (PARI) for(n=1,1e3, if(isprime(t=(n+1)^3 - n^2), print1(t", "))) \\ _Charles R Greathouse IV_, Sep 02 2016

%Y Cf. A140719, A005097, A154111, A154112.

%K nonn,easy

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Jan 04 2009