A027830 Numbers k such that k + (k+1)^2 + (k+2)^3 + (k+3)^4 + (k+4)^5 is prime.

1, 7, 11, 25, 35, 43, 45, 47, 51, 53, 57, 63, 65, 81, 91, 103, 113, 117, 121, 143, 149, 169, 173, 191, 193, 199, 201, 211, 213, 225, 235, 247, 253, 255, 263, 269, 299, 331, 333, 355, 357, 359, 373, 385, 387, 395, 399, 403, 411, 445, 453, 495, 519, 537, 579, 599

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• easy

Comments

Numbers k such that A027622(k) is prime.

Examples

			k=1: k + (k+1)^2 + (k+2)^3 + (k+3)^4 + (k+4)^5 = 3413 = A027886(1),
k=7: k + (k+1)^2 + (k+2)^3 + (k+3)^4 + (k+4)^5 = 171851 = A027886(2),
k=11: k + (k+1)^2 + (k+2)^3 + (k+3)^4 + (k+4)^5 = 800143 = A027886(3).
		

Links

• P. De Geest, Palindromic Quasi_Under_Squares of the form n+(n+1)^2

Crossrefs

Cf. A027622, A027886.

Programs

Magma

[n: n in [0..1000] |IsPrime(n+(n+1)^2+(n+2)^3+(n+3)^4+(n+4)^5)]; // Vincenzo Librandi, Nov 20 2010

Mathematica

With[{c=Total[Table[(#+i)^(i+1),{i,0,4}]]},Select[Range[600],PrimeQ[c]&]] (* Harvey P. Dale, May 07 2012 *)

PARI

is(n)=isprime(n+(n+1)^2+(n+2)^3+(n+3)^4+(n+4)^5) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

Edited by N. J. A. Sloane, May 21 2008 at the suggestion of R. J. Mathar