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

Author

Patrick De Geest, Feb 15 1999

Keywords

• nonn
• base

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).

Crossrefs

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

Programs

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 *)

PARI

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

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