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A010785 Repdigit numbers, or numbers with repeated digits. 85
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 222, 333, 444, 555, 666, 777, 888, 999, 1111, 2222, 3333, 4444, 5555, 6666, 7777, 8888, 9999, 11111, 22222, 33333, 44444, 55555, 66666, 77777, 88888, 99999, 111111, 222222, 333333, 444444, 555555, 666666 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A037904(a(n)) = 0. - Reinhard Zumkeller, Dec 14 2007

Complement of A139819. - David Wasserman, May 21 2008

Subsequence of A134336 and of A178403; A178401(a(n))>0. - Reinhard Zumkeller, May 27 2010

For n > 0: A193459(a(n)) = A000005(a(n)), subsequence of A193460;

for n > 10: a(n) mod 10 = floor(a(n)/10) mod 10, A010879(n)=A010879(A059995(n)). - Reinhard Zumkeller, Jul 26 2011

A202022(a(n)) = 1. - Reinhard Zumkeller, Dec 09 2011

A151949(a(n)) = 0; A180410(a(n)) = A227362(a(n)). - Reinhard Zumkeller, Jul 09 2013

A047842(a(n)) = A244112(a(n)). - Reinhard Zumkeller, Nov 11 2014

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Bart Goddard, Jeremy Rouse, Sum of two repdigits a square, arXiv:1607.06681 [math.NT], 2016. Mentions this sequence.

Eric Weisstein's World of Mathematics, Repdigit

Wikipedia, Repdigit

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, -10).

FORMULA

a(0)=0, a(1)=1, a(2)=2, a(3)=3, a(4)=4, a(5)=5, a(6)=6, a(7)=7, a(8)=8, a(9)=9, a(10)=11, a(11)=22, a(12)=33, a(13)=44, a(14)=55, a(15)=66, a(16)=77, a(17)=88, a(n)=11*a(n-9)-10*a(n-18). - Harvey P. Dale, Dec 28 2011

a(n) = (n-9*floor((n-1)/9))*(10^floor((n+8)/9)-1)/9. - José de Jesús Camacho Medina, Nov 06 2014

G.f.: x*(9*x^8+8*x^7+7*x^6+6*x^5+5*x^4+4*x^3+3*x^2+2*x+1)/((x^9-1)*(10*x^9-1)). - Robert Israel, Nov 09 2014

MAPLE

seq((n-9*floor(((n-1)/9)))*((10^(floor(((n+8)/9)))-1)/9), n = 1 .. 100); # Robert Israel, Nov 09 2014

MATHEMATICA

fQ[n_]:=Module[{id=IntegerDigits[n]}, Length[Union[id]]==1]; Select[Range[0, 10000], fQ] (* Vladimir Joseph Stephan Orlovsky, Dec 29 2010 *)

Union[FromDigits/@Flatten[Table[PadRight[{}, i, n], {n, 0, 9}, {i, 6}], 1]] (* or *) LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, -10}, {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88}, 40] (* Harvey P. Dale, Dec 28 2011 *)

Union@ Flatten@ Table[k (10^n - 1)/9, {k, 0, 9}, {n, 6}] (* Robert G. Wilson v, Oct 09 2014 *)

Table[(n - 9 Floor[(n - 1)/9]) (10^Floor[(n + 8)/9] - 1)/9, {n, 0, 50}]

(* José de Jesús Camacho Medina, Nov 06 2014 *)

PROG

(PARI) a(n)=10^((n+8)\9)\9*((n-1)%9+1) \\ Charles R Greathouse IV, Jun 15 2011

(PARI) nxt(n, t=n%10)=if(t<9, n*(t+1), n*10+9))\t \\ Yields the term a(k+1) following a given term a(k)=n. M. F. Hasler, Jun 24 2016

(PARI) is(n)={1==#Set(digits(n))}

inv(n) = 9*#Str(n) + n%10 - 9 \\ David A. Corneth, Jun 24 2016

(Haskell)

a010785 n = a010785_list !! n

a010785_list = 0 : r [1..9] where

   r (x:xs) = x : r (xs ++ [10*x + x `mod` 10])

-- Reinhard Zumkeller, Jul 26 2011

(MAGMA) [(n-9*Floor((n-1)/9))*(10^Floor((n+8)/9)-1)/9: n in [0..50]]; // Vincenzo Librandi, Nov 10 2014

CROSSREFS

Cf. A047842, A244112.

Sequence in context: A160818 A244514 A082810 * A032573 A190217 A222620

Adjacent sequences:  A010782 A010783 A010784 * A010786 A010787 A010788

KEYWORD

nonn,base,easy,nice

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified September 29 20:07 EDT 2016. Contains 276617 sequences.