login
A048334
Numbers that are repdigits in base 9.
3
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
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
KEYWORD
nonn,base
AUTHOR
Patrick De Geest, Feb 15 1999
STATUS
approved