A048334 Numbers that are repdigits in base 9.

0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 20, 30, 40, 50, 60, 70, 80, 91, 182, 273, 364, 455, 546, 637, 728, 820, 1640, 2460, 3280, 4100, 4920, 5740, 6560, 7381, 14762, 22143, 29524, 36905, 44286, 51667, 59048, 66430, 132860, 199290, 265720, 332150, 398580

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..800

Eric Weisstein's World of Mathematics, Repdigit.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,10,0,0,0,0,0,0,0,-9).

Formula

G.f.: x*(1+2*x+3*x^2+4*x^3+5*x^4+6*x^5+7*x^6+8*x^7) / ( (x-1) *(1+x) *(x^2+1) *(3*x^4-1) *(3*x^4+1) *(x^4+1) ). - R. J. Mathar, Mar 14 2015

a(n) = 10*a(n-8) -9*a(n-16). - R. J. Mathar, Mar 14 2015

Sum_{n>=1} 1/a(n) = (761/35) * A248726 = 3.02323812974071904119... - Amiram Eldar, Jan 21 2022

Mathematica

Union[Flatten[Table[FromDigits[PadRight[{}, n, d], 9], {n, 0, 40}, {d, 8}]]] (* Vincenzo Librandi, Feb 06 2014 *)
Table[FromDigits[IntegerDigits[(n-9*Floor[(n-1)/9])*(10^Floor[(n+8)/9]-1)/9], 9], {n, 0, 50}] (* Zak Seidov, Mar 15 2015 *)
f[n_] := Block[{r = FromDigits[#, 9] & /@ (Table[1, {#}] & /@ Range@ n)},
Sort@ Flatten[Times[r, #] & /@ Range@ 8]]; f[6] (* Michael De Vlieger, Mar 15 2015 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, -9}, {0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 20, 30, 40, 50, 60, 70}, 47] (* Ray Chandler, Jul 15 2015 *)

Prog

(PARI) lista(nn) = for (n=0, nn, if ((n==0) || (#Set(digits(n, 9)) == 1), print1(n, ", "))); \\ Michel Marcus, Mar 17 2015

Crossrefs

Cf. A010785, A033022, A028987, A028988, A248726.

Sequence in context: A297268 A048320 A037407 * A087027 A358142 A280770

Adjacent sequences: A048331 A048332 A048333 * A048335 A048336 A048337

Keyword

nonn,base

Author

Patrick De Geest, Feb 15 1999

Status

approved