A053700 a(n) = 111111 in base n.

6, 63, 364, 1365, 3906, 9331, 19608, 37449, 66430, 111111, 177156, 271453, 402234, 579195, 813616, 1118481, 1508598, 2000719, 2613660, 3368421, 4288306, 5399043, 6728904, 8308825, 10172526, 12356631, 14900788, 17847789, 21243690, 25137931

Offset

1,1

Links

Table of n, a(n) for n=1..30.

Carlos M. da Fonseca and Anthony G. Shannon, A formal operator involving Fermatian numbers, Notes Num. Theor. Disc. Math. (2024) Vol. 30, No. 3, 491-498.

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

Formula

a(n) = n^5 + n^4 + n^3 + n^2 + n + 1 = (n^6-1)/(n-1).

G.f.: x*(6 + 27*x + 76*x^2 + 6*x^3 + 6*x^4 - x^5)/(1-x)^6. - Colin Barker, May 08 2012

E.g.f.: exp(x)*(1 + 5*x + 26*x^2 + 32*x^3 + 11*x^4+ x^5) - 1. - Stefano Spezia, Oct 03 2024

Example

a(3)=364 because 111111 base 3 = 243 + 81 + 27 + 9 + 3 + 1 = 121.

Mathematica

Table[(n^5+n^4+n^3+n^2+n+1), {n, 0, 5!}] (* Vladimir Joseph Stephan Orlovsky, Mar 06 2010 *)

Prog

(PARI) a(n)=(n^6-1)/(n-1) \\ Charles R Greathouse IV, Sep 28 2015

Crossrefs

6th row of the array A055129.

Cf. A104878.

Sequence in context: A027811 A027950 A184447 * A296393 A123615 A245754

Adjacent sequences: A053697 A053698 A053699 * A053701 A053702 A053703

Keyword

base,nonn,easy

Author

Henry Bottomley, Mar 23 2000

Status

approved