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Primes of the form 3^k + 2^k - k^3 + k^2.
1

%I #13 Jan 23 2023 17:21:16

%S 2,5,17,613,129266611,7625731683761,150094704016430497,

%T 2503155504994422192936289397051173,

%U 4638397686588101984398752568803509060305779468709

%N Primes of the form 3^k + 2^k - k^3 + k^2.

%C The associated values of k are 0, 1,3,6,17,27,36,70,102,237,377,463,576,639,683,... [_R. J. Mathar_, Jun 12 2009] (* Amended by Harvey P. Dale, Jan 23 2023 *)

%C The next term (a(10)) has 114 digits. - _Harvey P. Dale_, Jan 23 2023

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

%t Select[Table[3^k+2^k-k^3+k^2,{k,0,200}],PrimeQ] (* _Harvey P. Dale_, Jan 23 2023 *)

%o (Magma) [ a: n in [1..450] | IsPrime(a) where a is 3^n+2^n-n^3+n^2] // _Vincenzo Librandi_, Nov 30 2010

%Y Cf. A058765, A082101, A161470.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Jun 10 2009

%E Definition simplified by _R. J. Mathar_, Jun 12 2009

%E a(1) = 2 prepended by _Harvey P. Dale_, Jan 23 2023