A048332 Numbers that are repdigits in base 7.

0, 1, 2, 3, 4, 5, 6, 8, 16, 24, 32, 40, 48, 57, 114, 171, 228, 285, 342, 400, 800, 1200, 1600, 2000, 2400, 2801, 5602, 8403, 11204, 14005, 16806, 19608, 39216, 58824, 78432, 98040, 117648, 137257, 274514, 411771, 549028, 686285, 823542, 960800

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..600

Eric Weisstein's World of Mathematics, Repdigit.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,8,0,0,0,0,0,-7).

Formula

From Chai Wah Wu, May 30 2016: (Start)

a(n) = 8*a(n-6) - 7*a(n-12) for n > 11.

G.f.: x*(6*x^5 + 5*x^4 + 4*x^3 + 3*x^2 + 2*x + 1)/(7*x^12 - 8*x^6 + 1). (End)

a(n) = (n - 6*floor((n-1)/6))*(7^floor((n+5)/6) - 1)/6. - Ilya Gutkovskiy, May 30 2016

Sum_{n>=1} 1/a(n) = (147/10) * A248724 = 2.80637791743084519957... - Amiram Eldar, Jan 21 2022

Mathematica

Union[Flatten[Table[FromDigits[PadRight[{}, n, d], 7], {n, 0, 40}, {d, 6}]]] (* Vincenzo Librandi, Feb 06 2014 *)
LinearRecurrence[{0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -7}, {0, 1, 2, 3, 4, 5, 6, 8, 16, 24, 32, 40}, 25] (* G. C. Greubel, May 30 2016 *)

Prog

(Python)
A048332_list = [0] + [int(d*l, 7) for l in range(1, 10) for d in '123456'] # Chai Wah Wu, May 30 2016

Crossrefs

Cf. A010785, A033020, A028987, A028988, A248724.

Sequence in context: A029954 A048318 A037402 * A249158 A119336 A133706

Adjacent sequences: A048329 A048330 A048331 * A048333 A048334 A048335

Keyword

nonn,base,easy

Author

Patrick De Geest, Feb 15 1999

Status

approved