A053717 a(n) = n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1.

1, 8, 255, 3280, 21845, 97656, 335923, 960800, 2396745, 5380840, 11111111, 21435888, 39089245, 67977560, 113522235, 183063616, 286331153, 435984840, 648232975, 943531280, 1347368421, 1891142968, 2613136835, 3559590240, 4785883225, 6357828776, 8353082583

Offset

0,2

Comments

a(n) = 11111111 in base n for n>0.

Links

Table of n, a(n) for n=0..26.

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 (8,-28,56,-70,56,-28,8,-1).

Formula

a(n) = (n^8-1)/(n-1) for n != 1.

G.f.: 1 -x*(x^7-8*x^6-57*x^5-1016*x^4-2297*x^3-1464*x^2-191*x-8)/(x-1)^8. - Colin Barker, Oct 29 2012

E.g.f.: exp(x)*(1 + 7*x + 120*x^2 + 423*x^3 + 426*x^4 + 156*x^5 + 22*x^6 + x^7). - Stefano Spezia, Oct 03 2024

Example

a(3) = 3280 because 11111111 base 3 = 2187+729+243+81+27+9+3+1 = 3280.

Mathematica

Table[FromDigits["11111111", n], {n, 1, 30}] (* or *) Table[n^7+n^6+n^5+n^4+n^3+n^2+n+1, {n, 1, 60}] (* Vladimir Joseph Stephan Orlovsky, Jan 29 2012 *)

Crossrefs

8th row of the array A055129.

Cf. A104878.

Sequence in context: A226428 A277421 A171612 * A267250 A034674 A317511

Adjacent sequences: A053714 A053715 A053716 * A053718 A053719 A053720

Keyword

nonn,base,easy

Author

Henry Bottomley, Mar 23 2000

Extensions

a(0)=1 prepended by Alois P. Heinz, May 04 2021

Status

approved