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

Author

Patrick De Geest, Feb 15 1999

Keywords

• nonn
• base

Examples

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..500
• Eric Weisstein's World of Mathematics, Repdigit.

Crossrefs

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

Programs

Magma

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

Mathematica

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

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