A048331 Numbers that are repdigits in base 6.

0, 1, 2, 3, 4, 5, 7, 14, 21, 28, 35, 43, 86, 129, 172, 215, 259, 518, 777, 1036, 1295, 1555, 3110, 4665, 6220, 7775, 9331, 18662, 27993, 37324, 46655, 55987, 111974, 167961, 223948, 279935, 335923, 671846, 1007769, 1343692, 1679615, 2015539

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..500

Eric Weisstein's World of Mathematics, Repdigit.

Formula

Conjecture: G.f.: x*(1+2*x+3*x^2+4*x^3+5*x^4) / ( (x-1)*(x^4+x^3+x^2+x+1)*(6*x^5-1) ) with a(n) = 7*a(n-5) - 6*a(n-10). - R. J. Mathar, Mar 15 2015

Sum_{n>=1} 1/a(n) = (137/12) * A248723 = 2.67320256903907177403... - Amiram Eldar, Jan 21 2022

Example

14_10 = 22_6, 21_10_ = 33_6, 9331_10_ = 111111_6.

Mathematica

Union[Flatten[Table[FromDigits[PadRight[{}, n, d], 6], {n, 0, 40}, {d, 5}]]] (* Vincenzo Librandi, Feb 06 2014 *)

Prog

(Magma) [0] cat [k:k in [1..2*10^6]| #Set(Intseq(k, 6)) eq 1]; // Marius A. Burtea, Oct 11 2019

Crossrefs

Cf. A010785, A033019, A028987, A028988, A248723.

Sequence in context: A029953 A048317 A037398 * A133476 A131023 A069514

Adjacent sequences: A048328 A048329 A048330 * A048332 A048333 A048334

Keyword

nonn,base

Author

Patrick De Geest, Feb 15 1999

Status

approved