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

0,2

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).

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

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 *)

Prog

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

Crossrefs

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

Cf. A002283, A059482.

Cf. A008591 (digits sums).

Sequence in context: A328089 A186527 A178511 * A034993 A223328 A093281

Adjacent sequences: A184334 A184335 A184336 * A184338 A184339 A184340

Keyword

nonn,easy,base

Author

Paul Curtz, Feb 13 2011

Status

approved