A242436 n^5 - 2n.

0, -1, 28, 237, 1016, 3115, 7764, 16793, 32752, 59031, 99980, 161029, 248808, 371267, 537796, 759345, 1048544, 1419823, 1889532, 2476061, 3199960, 4084059, 5153588, 6436297, 7962576, 9765575, 11881324, 14348853, 17210312, 20511091, 24299940, 28629089, 33554368, 39135327, 45435356

Offset

0,3

Comments

For n > 0, a(n) is the largest number k such that k^5 + n is divisible by k + n, or -1 if k is infinite. When k = n^5 - 2n, (k^5 + n)/(k + n) = n^20 - 9n^16 + 31n^12 - 49n^8 + 31n^4 - 1.

For n > 1 and j > 0, the largest number k such that k^(2j+1) + n is divisible by k + n is given by k = n^(2j+1) - 2n.

For n > 1, a(n) is also the largest number k such that k + n^5 is divisible by k + n. - Derek Orr, Oct 16 2014

Links

Michael De Vlieger, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

From Wesley Ivan Hurt, Aug 17 2014: (Start)

G.f.: (-x+34*x^2+54*x^3+34*x^4-x^5) / (x-1)^6;

a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6);

a(n) = A000584(n) - A005843(n). (End)

Example

a(2) = 28. 28 is the largest number k such that k^5 + 2 is divisible by k + 2. The resulting integer is 573679 = 2^20 - 9*2^16 + 31*2^12 - 49*2^8 + 31*2^4 - 1.

Maple

A242436:=n->n^5-2*n: seq(A242436(n), n=0..30); # Wesley Ivan Hurt, Aug 17 2014

Mathematica

Table[n^5 - 2 n, {n, 0, 30}] (* Wesley Ivan Hurt, Aug 17 2014 *)
CoefficientList[Series[(-x + 34 x^2 + 54 x^3 + 34 x^4 - x^5)/(-1 + x)^6, {x, 0, 30}], x] (* Wesley Ivan Hurt, Aug 17 2014 *)
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, -1, 28, 237, 1016, 3115}, 40] (* Harvey P. Dale, Apr 07 2017 *)

Prog

(PARI) vector(100, n, (n-1)^5 - 2*(n-1))
(Magma) [n^5-2*n: n in [0..35]]; // Vincenzo Librandi, Oct 17 2014

Crossrefs

Cf. A000584, A005843, A242135.

Sequence in context: A138405 A024015 A223347 * A119544 A112797 A085438

Adjacent sequences: A242433 A242434 A242435 * A242437 A242438 A242439

Keyword

sign,easy

Author

Derek Orr, Aug 16 2014

Status

approved