A100357
Numbers k such that 2^k + k^2 + 1 is prime.
Original entry on oeis.org
0, 6, 12, 18, 162, 192, 216, 420, 1524, 5112, 7404, 24216, 25944, 101832, 346854
Offset: 1
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[n: n in [0..800] | IsPrime(2^n + n^2 + 1) ]; // Vincenzo Librandi, Sep 03 2012
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{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 *)
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is(n)=isprime(2^n+n^2+1) \\ Charles R Greathouse IV, Jul 01 2013
Mathematica codes edited by
Zak Seidov, Apr 05 2014
A215434
Primes of form 2^k + k^2 - 1.
Original entry on oeis.org
2, 7, 31, 1123, 1180591620717411308323, 21778071482940061661655974875633165551139, 89202980794122492566142873090593446023942979, 1569275433846670190958947355801916604025588861116008664323
Offset: 1
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[a: n in [0..250] | IsPrime(a) where a is 2^n+n^2-1];
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Select[Table[2^n + n^2 - 1, {n, 0, 300}], PrimeQ]
A182357
Primes of the form 2^n + n^2 + 2.
Original entry on oeis.org
3, 5, 19, 59, 179, 8363, 131363, 134218459, 2147484611, 49039857307708443467467104868809893875799651909875303859, 3291009114642412084309938365114701009965471731267159726697262571
Offset: 1
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Select[Table[2^n+n^2+2,{n,1000}],PrimeQ] (* Harvey P. Dale, Jul 22 2012 *)
A216592
Numbers m such that 8^m + m^8 + 1 is prime.
Original entry on oeis.org
8^0 + 0^8 + 1 = 2, which is prime, so 0 is in the sequence.
Cf. Numbers m such that k^m + m^k - 1 is prime:
A215439 (k=2),
A215440 (k=3),
A216424 (k=4),
A215443 (k=5),
A216425 (k=6),
A215445 (k=7),
A216591 (k=8),
A216619 (k=10),
A215446 (k=11),
A216420 (k=13),
A216422 (k=19).
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Select[Range[0, 10000], PrimeQ[8^# + #^8 + 1] &]
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is(n)=ispseudoprime(8^n+n^8+1) \\ Charles R Greathouse IV, Jun 13 2017
Showing 1-4 of 4 results.
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