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A100357 Numbers k such that 2^k + k^2 + 1 is prime. 20

%I #22 Sep 08 2022 08:45:15

%S 0,6,12,18,162,192,216,420,1524,5112,7404,24216,25944,101832,346854

%N Numbers k such that 2^k + k^2 + 1 is prime.

%C a(15) > 200000. - _Giovanni Resta_, Mar 23 2014

%C All terms are multiples of 6. Corresponding primes of the form 2^n+n^2+1 are in A035325. - _Zak Seidov_, Apr 05 2014

%C a(16) > 5*10^5. - _Robert Price_, Jun 15 2014

%t {ta={{0}}, tb={{0}}}; Do[g=n;s=2^n+n^2+1;If[PrimeQ[s], Print[n];ta=Append[ta, n];tb=Append[tb, s]], {n, 0, 10000, 6}];{ta, tb, g}

%t Select[Range[0, 10000, 6], PrimeQ[2^# + #^2 + 1] &] (* _Vincenzo Librandi_, Sep 03 2012 *)

%o (Magma) [n: n in [0..800] | IsPrime(2^n + n^2 + 1) ] // _Vincenzo Librandi_, Sep 03 2012

%o (PARI) is(n)=isprime(2^n+n^2+1) \\ _Charles R Greathouse IV_, Jul 01 2013

%Y Cf. A001580, A063997, A035325.

%K nonn

%O 1,2

%A _Labos Elemer_, Nov 19 2004

%E Added a(1) from _Vincenzo Librandi_, Sep 03 2012

%E a(12)-a(14) from _Giovanni Resta_, Mar 23 2014

%E Mathematica codes edited by _Zak Seidov_, Apr 05 2014

%E a(15) from _Robert Price_, Jun 15 2014

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)