A048332 Numbers that are repdigits in base 7.
0, 1, 2, 3, 4, 5, 6, 8, 16, 24, 32, 40, 48, 57, 114, 171, 228, 285, 342, 400, 800, 1200, 1600, 2000, 2400, 2801, 5602, 8403, 11204, 14005, 16806, 19608, 39216, 58824, 78432, 98040, 117648, 137257, 274514, 411771, 549028, 686285, 823542, 960800
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..600
- Eric Weisstein's World of Mathematics, Repdigit.
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,8,0,0,0,0,0,-7).
Programs
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Mathematica
Union[Flatten[Table[FromDigits[PadRight[{}, n, d], 7], {n, 0, 40}, {d, 6}]]] (* Vincenzo Librandi, Feb 06 2014 *) LinearRecurrence[{0,0,0,0,0,8,0,0,0,0,0,-7},{0, 1, 2, 3, 4, 5, 6, 8, 16, 24, 32, 40}, 25] (* G. C. Greubel, May 30 2016 *) -
Python
A048332_list = [0] + [int(d*l,7) for l in range(1,10) for d in '123456'] # Chai Wah Wu, May 30 2016
Formula
From Chai Wah Wu, May 30 2016: (Start)
a(n) = 8*a(n-6) - 7*a(n-12) for n > 11.
G.f.: x*(6*x^5 + 5*x^4 + 4*x^3 + 3*x^2 + 2*x + 1)/(7*x^12 - 8*x^6 + 1). (End)
a(n) = (n - 6*floor((n-1)/6))*(7^floor((n+5)/6) - 1)/6. - Ilya Gutkovskiy, May 30 2016
Sum_{n>=1} 1/a(n) = (147/10) * A248724 = 2.80637791743084519957... - Amiram Eldar, Jan 21 2022