A048329 Numbers that are repdigits in base 4.

0, 1, 2, 3, 5, 10, 15, 21, 42, 63, 85, 170, 255, 341, 682, 1023, 1365, 2730, 4095, 5461, 10922, 16383, 21845, 43690, 65535, 87381, 174762, 262143, 349525, 699050, 1048575, 1398101, 2796202, 4194303, 5592405, 11184810, 16777215, 22369621, 44739242, 67108863

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Eric Weisstein's World of Mathematics, Repdigit.

Index entries for linear recurrences with constant coefficients, signature (0,0,5,0,0,-4).

Formula

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

Sum_{n>=1} 1/a(n) = (11/2) * A248721 = 2.31603727318383077512... - Amiram Eldar, Jan 21 2022

Example

10_10 = 22_4, 15_10 = 33_4, 5461_10 = 1111111_4.

Maple

a:= n-> (1+irem(n+2, 3))*(4^iquo(n+2, 3)-1)/3:
seq(a(n), n = 0..45);

Mathematica

Union[Flatten[Table[FromDigits[PadRight[{}, n, d], 4], {n, 0, 40}, {d, 3}]]](* Vincenzo Librandi, Feb 06 2014 *)
LinearRecurrence[{0, 0, 5, 0, 0, -4}, {0, 1, 2, 3, 5, 10}, 40] (* Harvey P. Dale, Jul 11 2023 *)

Prog

(Magma) [0] cat  [k:k in [1..10^7]| #Set(Intseq(k, 4)) eq 1]; // Marius A. Burtea, Oct 11 2019

Crossrefs

Cf. A010785, A033017, A028987, A028988, A248721.

Base 4 repdigits 1,2,3 (trisections): A002450, A020988, A024036.

Sequence in context: A043851 A043859 A043868 * A252659 A004691 A133335

Adjacent sequences: A048326 A048327 A048328 * A048330 A048331 A048332

Keyword

nonn,base,easy

Author

Patrick De Geest, Feb 15 1999

Status

approved