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%I #43 Oct 31 2022 02:09:28
%S 0,1,11,12,121,122,132,133,1331,1332,1342,1343,1452,1453,1463,1464,
%T 14641,14642,14652,14653,14762,14763,14773,14774,15972,15973,15983,
%U 15984,16093,16094,16104,16105,161051,161052,161062,161063,161172
%N Sums of distinct powers of 11.
%C Numbers without any base-11 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="/A033047/b033047.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)*11^i, where Sum_{i=0..m} d(i)*2^i is the base-2 representation of n.
%F a(n) = A097257(n)/10.
%F a(2n) = 11*a(n), a(2n+1) = a(2n)+1.
%F a(n) = Sum_{k>=0} A030308(n,k)*11^k. - _Philippe Deléham_, Oct 17 2011
%F G.f.: (1/(1 - x))*Sum_{k>=0} 11^k*x^(2^k)/(1 + x^(2^k)). - _Ilya Gutkovskiy_, Jun 04 2017
%t With[{k = 11}, Map[FromDigits[#, k] &, Tuples[{0, 1}, 6]]] (* _Michael De Vlieger_, Oct 28 2022 *)
%o (PARI) {for(vv=0,35,
%o bvv=binary(vv);
%o texp=0;btb=0;
%o forstep(i=length(bvv),1,-1,btb=btb+bvv[i]*11^texp;texp++);
%o print1(btb,", "))} \\ _Douglas Latimer_, May 12 2012
%o (PARI) a(n)=fromdigits(binary(n),11) \\ _Charles R Greathouse IV_, Jan 11 2017
%Y Cf. A000695, A005836, A033042-A033052.
%Y Row 10 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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