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A048337 a(n) in base 13 is a repdigit. 2

%I #25 May 30 2016 18:26:14

%S 0,1,2,3,4,5,6,7,8,9,10,11,12,14,28,42,56,70,84,98,112,126,140,154,

%T 168,183,366,549,732,915,1098,1281,1464,1647,1830,2013,2196,2380,4760,

%U 7140,9520,11900,14280,16660,19040,21420,23800,26180,28560,30941,61882

%N a(n) in base 13 is a repdigit.

%C Integers n such that A043540(n)=1. - _Michel Marcus_, Aug 19 2015

%H Vincenzo Librandi, <a href="/A048337/b048337.txt">Table of n, a(n) for n = 0..1200</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Repdigit.html">Repdigit</a>

%F From _Chai Wah Wu_, May 30 2016: (Start)

%F a(n) = 14*a(n-12) - 13*a(n-24) for n > 23.

%F G.f.: x*(12*x^11 + 11*x^10 + 10*x^9 + 9*x^8 + 8*x^7 + 7*x^6 + 6*x^5 + 5*x^4 + 4*x^3 + 3*x^2 + 2*x + 1)/(13*x^24 - 14*x^12 + 1). (End)

%F a(n) = (n - 12*floor((n-1)/12))*(13^floor((n+11)/12) - 1)/12. - _Ilya Gutkovskiy_, May 30 2016

%t Union[Flatten[Table[FromDigits[PadRight[{}, n, d], 13], {n, 0, 50}, {d, 12}]]] (* _Vincenzo Librandi_, Feb 06 2014 *)

%o (PARI) isok(n) = !n || (#vecsort(digits(n,13),,8) == 1) \\ _Michel Marcus_, Aug 19 2015

%o (Python)

%o A048337_list = [0] + [int(d*l,13) for l in range(1,10) for d in '123456789abc'] # _Chai Wah Wu_, May 30 2016

%Y Cf. A010785, A033026, A028987, A028988, A043540.

%K nonn,base,easy

%O 0,3

%A _Patrick De Geest_, Feb 15 1999

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Last modified April 25 06:35 EDT 2024. Contains 371964 sequences. (Running on oeis4.)