A184337 a(n) is the integer whose decimal representation consists of n 8's followed by n 1's.

0, 81, 8811, 888111, 88881111, 8888811111, 888888111111, 88888881111111, 8888888811111111, 888888888111111111, 88888888881111111111, 8888888888811111111111, 888888888888111111111111, 88888888888881111111111111

Offset: 0

Author

Paul Curtz, Feb 13 2011

Keywords

• nonn
• easy
• base

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Richard Blecksmith and Charles Nicol, Monotonic Numbers, Mathematics Magazine, 66, (1993), 257-262.
• Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

Crossrefs

Cf. A098210 (with 1 and 5 instead of 8 and 1).

Cf. A002283, A059482.

Cf. A008591 (digits sums).

Programs

Magma

[(8*100^n-7*10^n-1)/9: n in [0..20]]; // Vincenzo Librandi, Aug 04 2011

Mathematica

Table[(8*100^n - 7*10^n - 1)/9, {n,0,30}] (* G. C. Greubel, Nov 02 2018 *)
FromDigits/@Table[Join[PadRight[{},n,8],PadRight[{},n,1]],{n,0,15}] (* or *) LinearRecurrence[ {111,-1110,1000},{0,81,8811},15] (* Harvey P. Dale, Jul 03 2023 *)

PARI

vector(30, n, n--; (8*100^n - 7*10^n - 1)/9) \\ G. C. Greubel, Nov 02 2018

Python

for n in range(30):
    print((8*100**n-7*10**n-1)//9, end=', ')
# Stefano Spezia, Nov 02 2018

Formula

a(n) = (8*100^n - 7*10^n - 1)/9.

a(n) = A059482(n)*A002283(n).

G.f.: 9*x*(-9+20*x) / ( (x-1)*(100*x-1)*(10*x-1) ). - R. J. Mathar, Feb 28 2011