A053699 a(n) = n^4 + n^3 + n^2 + n + 1.

1, 5, 31, 121, 341, 781, 1555, 2801, 4681, 7381, 11111, 16105, 22621, 30941, 41371, 54241, 69905, 88741, 111151, 137561, 168421, 204205, 245411, 292561, 346201, 406901, 475255, 551881, 637421, 732541, 837931, 954305, 1082401, 1222981

Offset

0,2

Comments

a(n) = 11111 in base n.

a(n) = Phi_5(n), where Phi_k is the k-th cyclotomic polynomial.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Michael Penn, What base makes me a perfect square??, YouTube video, 2022.

Index to values of cyclotomic polynomials of integer argument

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = n^4 + n^3 + n^2 + n + 1 =(n^5-1)/(n-1).

G.f.: (1 + 16*x^2 + 6*x^3 + x^4)/(1-x)^5. - Colin Barker, Jan 10 2012

Maple

A053699 := proc(n)
        numtheory[cyclotomic](5, n) ;
end proc:
seq(A053699(n), n=0..20) ; # R. J. Mathar, Feb 07 2014

Mathematica

f[n_]:=((1+n+n^2+n^3+n^4)); Table[f[n], {n, 0, 6!}] (* Vladimir Joseph Stephan Orlovsky, Mar 03 2010 *)
Join[{1}, Table[Total[n^Range[0, 4]], {n, 40}]] (* Harvey P. Dale, Feb 02 2014 *)

Prog

(Magma) [n^4+n^3+n^2+n+1: n in [0..50]]; // Vincenzo Librandi, May 01 2011
(PARI) a(n)=polcyclo(5, n) \\ Charles R Greathouse IV, Jul 19 2011
(Maxima) A053699(n):=n^4 + n^3 + n^2 + n + 1$
makelist(A053699(n), n, 0, 30); /* Martin Ettl, Nov 07 2012 */

Crossrefs

Sequence in context: A099083 A212523 A096944 * A152122 A260045 A267938

Adjacent sequences: A053696 A053697 A053698 * A053700 A053701 A053702

Keyword

nonn,easy

Author

Henry Bottomley, Mar 23 2000

Status

approved