A137950 Numbers k such that k^0 + (k+1)^1 + (k+2)^2 + (k+3)^3 + (k+4)^4 is a prime.

1, 3, 4, 5, 7, 11, 14, 21, 22, 23, 28, 31, 33, 47, 50, 53, 56, 59, 70, 72, 82, 88, 92, 99, 106, 120, 122, 124, 135, 140, 149, 157, 159, 162, 166, 169, 172, 179, 182, 205, 217, 218, 224, 225, 229, 231, 239, 243, 247, 249, 256, 257, 262, 263, 273, 283, 284, 290, 302

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, May 06 2008

Keywords

• nonn

Comments

Numbers k such that k^4 + 17*k^3 + 106*k^2 + 288*k + 289 is prime. - Robert Israel, Jul 21 2020

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Programs

Magma

[n: n in [0..500] | IsPrime(n^0+(n+1)^1+(n+2)^2+(n+3)^3+(n+4)^4)]; // Vincenzo Librandi, Nov 24 2010

Maple

filter:= k -> isprime(k^4 + 17*k^3 + 106*k^2 + 288*k + 289):
select(filter, [$1..1000]); # Robert Israel, Jul 21 2020

Mathematica

a={};Do[If[PrimeQ[n^0+(n+1)^1+(n+2)^2+(n+3)^3+(n+4)^4],AppendTo[a,n]],{n,10^2*2}];a
Select[Range[350],PrimeQ[Total[Table[(#+d)^d,{d,0,4}]]]&] (* Harvey P. Dale, Sep 01 2024 *)

Extensions

More terms from Vincenzo Librandi, Mar 26 2010