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A048329 Numbers that are repdigits in base 4.

%I A048329 #58 Feb 16 2025 08:32:39
%S A048329 0,1,2,3,5,10,15,21,42,63,85,170,255,341,682,1023,1365,2730,4095,5461,
%T A048329 10922,16383,21845,43690,65535,87381,174762,262143,349525,699050,
%U A048329 1048575,1398101,2796202,4194303,5592405,11184810,16777215,22369621,44739242,67108863
%N A048329 Numbers that are repdigits in base 4.
%H A048329 Vincenzo Librandi, <a href="/A048329/b048329.txt">Table of n, a(n) for n = 0..300</a>
%H A048329 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Repdigit.html">Repdigit</a>.
%H A048329 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,5,0,0,-4).
%F A048329 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
%F A048329 Sum_{n>=1} 1/a(n) = (11/2) * A248721 = 2.31603727318383077512... - _Amiram Eldar_, Jan 21 2022
%e A048329 10_10 = 22_4, 15_10 = 33_4, 5461_10 = 1111111_4.
%p A048329 a:= n-> (1+irem(n+2, 3))*(4^iquo(n+2,3)-1)/3:
%p A048329 seq(a(n), n = 0..45);
%t A048329 Union[Flatten[Table[FromDigits[PadRight[{}, n, d], 4], {n, 0, 40}, {d, 3}]]](* _Vincenzo Librandi_, Feb 06 2014 *)
%t A048329 LinearRecurrence[{0,0,5,0,0,-4},{0,1,2,3,5,10},40] (* _Harvey P. Dale_, Jul 11 2023 *)
%o A048329 (Magma) [0] cat  [k:k in [1..10^7]| #Set(Intseq(k,4)) eq 1]; // _Marius A. Burtea_, Oct 11 2019
%Y A048329 Cf. A010785, A033017, A028987, A028988, A248721.
%Y A048329 Base 4 repdigits 1,2,3 (trisections): A002450, A020988, A024036.
%K A048329 nonn,base,easy
%O A048329 0,3
%A A048329 _Patrick De Geest_, Feb 15 1999