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A100357
Numbers k such that 2^k + k^2 + 1 is prime.
20
0, 6, 12, 18, 162, 192, 216, 420, 1524, 5112, 7404, 24216, 25944, 101832, 346854
OFFSET
1,2
COMMENTS
a(15) > 200000. - Giovanni Resta, Mar 23 2014
All terms are multiples of 6. Corresponding primes of the form 2^n+n^2+1 are in A035325. - Zak Seidov, Apr 05 2014
a(16) > 5*10^5. - Robert Price, Jun 15 2014
MATHEMATICA
{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}
Select[Range[0, 10000, 6], PrimeQ[2^# + #^2 + 1] &] (* Vincenzo Librandi, Sep 03 2012 *)
PROG
(Magma) [n: n in [0..800] | IsPrime(2^n + n^2 + 1) ] // Vincenzo Librandi, Sep 03 2012
(PARI) is(n)=isprime(2^n+n^2+1) \\ Charles R Greathouse IV, Jul 01 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Nov 19 2004
EXTENSIONS
Added a(1) from Vincenzo Librandi, Sep 03 2012
a(12)-a(14) from Giovanni Resta, Mar 23 2014
Mathematica codes edited by Zak Seidov, Apr 05 2014
a(15) from Robert Price, Jun 15 2014
STATUS
approved