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Write A003512(n) in the base {1, 3, 4, 11, 15, 41, 56, 153, 209, ...} (see A002530).
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%I #17 Dec 30 2018 19:19:32

%S 10,110,1000,1010,10010,10110,11000,11010,20010,20110,100000,100010,

%T 100110,101000,101010,1000010,1000110,1001000,1001010,1010010,1010110,

%U 1011000,1011010,1020010,1020110,1100000,1100010,1100110,1101000,1101010,2000010,2000110

%N Write A003512(n) in the base {1, 3, 4, 11, 15, 41, 56, 153, 209, ...} (see A002530).

%H Rémy Sigrist, <a href="/A276387/b276387.txt">Table of n, a(n) for n = 1..1000</a>

%H Aviezri S. Fraenkel, Jonathan Levitt, Michael Shimshoni, <a href="http://dx.doi.org/10.1016/0012-365X(72)90012-X">Characterization of the set of values f(n)=[n alpha], n=1,2,...</a>, Discrete Math. 2 (1972), no. 4, 335-345. See Table 1.

%o (PARI) A002530(n) = contfracpnqn(vector(n, i, 1+(i>1)*(i%2)))[2, 1]

%o A003512(n) = floor(n*(sqrt(3)+2))

%o a(n) = my (v=A003512(n)); for (b=2, oo, if (v<=A002530(b), my (w=0); forstep (p=b, 2, -1, w=10*w + (v\A002530(p)); v=v%A002530(p)); return (w))) \\ _Rémy Sigrist_, Dec 29 2018

%Y Cf. A002530, A003511, A003512, A276386, A276388.

%K nonn,base

%O 1,1

%A _N. J. A. Sloane_, Sep 04 2016

%E More terms from _Rémy Sigrist_, Dec 29 2018