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A048329
Numbers that are repdigits in base 4.
5
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
Eric Weisstein's World of Mathematics, Repdigit.
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
Base 4 repdigits 1,2,3 (trisections): A002450, A020988, A024036.
Sequence in context: A043851 A043859 A043868 * A252659 A004691 A133335
KEYWORD
nonn,base,easy
AUTHOR
Patrick De Geest, Feb 15 1999
STATUS
approved