A048330 Numbers that are repdigits in base 5.

0, 1, 2, 3, 4, 6, 12, 18, 24, 31, 62, 93, 124, 156, 312, 468, 624, 781, 1562, 2343, 3124, 3906, 7812, 11718, 15624, 19531, 39062, 58593, 78124, 97656, 195312, 292968, 390624, 488281, 976562, 1464843, 1953124, 2441406, 4882812, 7324218, 9765624

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..400

Adriana Mora and Eric Bravo, On b-repdigit polygonal numbers, Notes Num. Theory Disc. Math. (2025) Vol. 31, No. 4, 819-828. See p. 820, Table 1.

Eric Weisstein's World of Mathematics, Repdigit.

Formula

Conjecture: G.f.: x*(1+2*x+3*x^2+4*x^3) / ( (x-1)*(1+x)*(x^2+1)*(5*x^4-1) ) with a(n) = 6*a(n-4) - 5*a(n-8). - R. J. Mathar, Mar 15 2015

Sum_{n>=1} 1/a(n) = (25/3) * A248722 = 2.51444877998310381623... - Amiram Eldar, Jan 21 2022

Example

12_10 = 22_5, 18_10 = 33_5, 7812_10 = 222222_5.

Mathematica

Union[Flatten[Table[FromDigits[PadRight[{}, n, d], 5], {n, 0, 40}, {d, 4}]]] (* Vincenzo Librandi, Feb 06 2014 *)

Prog

(Magma) [0] cat [k:k in [1..10^7]| #Set(Intseq(k, 5)) eq 1]; // Marius A. Burtea, Oct 11 2019

Crossrefs

Cf. A010785, A033018, A028987, A028988, A248722.

Sequence in context: A140494 A048316 A037393 * A118651 A206292 A129297

Adjacent sequences: A048327 A048328 A048329 * A048331 A048332 A048333

Keyword

nonn,base

Author

Patrick De Geest, Feb 15 1999

Extensions

Offset changed from 1 to 0 by Vincenzo Librandi, Feb 06 2014

Status

approved