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%I A033048 #49 Feb 16 2025 08:32:36
%S A033048 0,1,12,13,144,145,156,157,1728,1729,1740,1741,1872,1873,1884,1885,
%T A033048 20736,20737,20748,20749,20880,20881,20892,20893,22464,22465,22476,
%U A033048 22477,22608,22609,22620,22621,248832,248833,248844,248845,248976
%N A033048 Sums of distinct powers of 12.
%C A033048 Numbers without any base-12 digits greater than 1.
%H A033048 T. D. Noe, <a href="/A033048/b033048.txt">Table of n, a(n) for n = 0..1023</a>
%H A033048 Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, <a href="https://arxiv.org/abs/2210.10968">Identities and periodic oscillations of divide-and-conquer recurrences splitting at half</a>, arXiv:2210.10968 [cs.DS], 2022, p. 45.
%H A033048 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Duodecimal.html">Duodecimal</a>
%H A033048 Wikipedia, <a href="http://en.wikipedia.org/wiki/Duodecimal">Duodecimal</a>
%F A033048 a(n) = Sum_{i=0..m} d(i)*12^i, where Sum_{i=0..m} d(i)*2^i is the base-2 representation of n.
%F A033048 a(n) = A097258(n)/11.
%F A033048 a(2n) = 12*a(n), a(2n+1) = a(2n)+1.
%F A033048 a(n) = Sum_{k>=0} A030308(n,k)*b(k) with b(k) = 12^k = A001021(k). - _Philippe Deléham_, Oct 19 2011
%F A033048 G.f.: (1/(1 - x))*Sum_{k>=0} 12^k*x^(2^k)/(1 + x^(2^k)). - _Ilya Gutkovskiy_, Jun 04 2017
%t A033048 With[{k = 12}, Map[FromDigits[#, k] &, Tuples[{0, 1}, 6]]] (* _Michael De Vlieger_, Oct 28 2022 *)
%o A033048 (PARI) {maxn=37;
%o A033048 for(vv=0,maxn,
%o A033048 bvv=binary(vv);
%o A033048 ll=length(bvv);texp=0;btod=0;
%o A033048 forstep(i=ll,1,-1,btod=btod+bvv[i]*12^texp;texp++);
%o A033048 print1(btod,", "))}
%o A033048 \\ _Douglas Latimer_, Apr 16 2012
%o A033048 (PARI) a(n)=fromdigits(binary(n),12) \\ _Charles R Greathouse IV_, Jan 11 2017
%o A033048 (Haskell)
%o A033048 import Data.List (unfoldr)
%o A033048 a033048 n = a033048_list !! (n-1)
%o A033048 a033048_list = filter (all (< 2) . unfoldr (\x ->
%o A033048    if x == 0 then Nothing else Just $ swap $ divMod x 12)) [1..]
%o A033048 -- _Reinhard Zumkeller_, Apr 17 2011
%Y A033048 Subsequence of A102487.
%Y A033048 Cf. A000695, A005836, A033042-A033052.
%Y A033048 Row 11 of array A104257.
%K A033048 nonn,base,easy,changed
%O A033048 0,3
%A A033048 _Clark Kimberling_
%E A033048 Extended by _Ray Chandler_, Aug 03 2004

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