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%I #43 Oct 31 2022 02:09:46
%S 0,1,13,14,169,170,182,183,2197,2198,2210,2211,2366,2367,2379,2380,
%T 28561,28562,28574,28575,28730,28731,28743,28744,30758,30759,30771,
%U 30772,30927,30928,30940,30941,371293,371294,371306,371307,371462
%N Sums of distinct powers of 13.
%C Numbers without any base-13 digits greater than 1.
%C a(n) modulo 2 is the Prouhet-Thue-Morse sequence A010060. - _Philippe Deléham_, Oct 17 2011
%H T. D. Noe, <a href="/A033049/b033049.txt">Table of n, a(n) for n = 0..1023</a>
%H 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.
%F a(n) = Sum_{i=0..m} d(i)*13^i, where Sum_{i=0..m} d(i)*2^i is the base-2 representation of n.
%F a(n) = A097259(n)/12.
%F a(2n) = 13*a(n), a(2n+1) = a(2n)+1.
%F a(n) = Sum_{k>=0} A030308(n,k)*13^k. - _Philippe Deléham_, Oct 17 2011
%F G.f.: (1/(1 - x))*Sum_{k>=0} 13^k*x^(2^k)/(1 + x^(2^k)). - _Ilya Gutkovskiy_, Jun 04 2017
%t With[{k = 13}, Map[FromDigits[#, k] &, Tuples[{0, 1}, 6]]] (* _Michael De Vlieger_, Oct 28 2022 *)
%o (PARI) A033049(n,b=13)=subst(Pol(binary(n)),'x,b) \\ _M. F. Hasler_, Feb 01 2016
%Y Cf. A000695, A005836, A033042-A033052.
%Y Row 12 of array A104257.
%K nonn,base,easy
%O 0,3
%A _Clark Kimberling_
%E Extended by _Ray Chandler_, Aug 03 2004
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