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A048331
Numbers that are repdigits in base 6.
4
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
0,3
LINKS
Eric Weisstein's World of Mathematics, Repdigit.
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
EXAMPLE
14_10 = 22_6, 21_10_ = 33_6, 9331_10_ = 111111_6.
MATHEMATICA
Union[Flatten[Table[FromDigits[PadRight[{}, n, d], 6], {n, 0, 40}, {d, 5}]]] (* Vincenzo Librandi, Feb 06 2014 *)
PROG
(Magma) [0] cat [k:k in [1..2*10^6]| #Set(Intseq(k, 6)) eq 1]; // Marius A. Burtea, Oct 11 2019
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Patrick De Geest, Feb 15 1999
STATUS
approved