This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A071915 #12 Sep 05 2020 07:46:11 %S A071915 0,0,1,0,2,3,3,6,3,5,1,2,8,2,3,5,2,3,3,6,10,8,6,4,2,3,6,5,2,9,12,7,17, %T A071915 10,7,9,8,10,13,13,10,12,14,9,11,10,11,6,9,5,3,13,13,19,18,13,8,12,15, %U A071915 14,18,7,19,19,17,15,13,14,16,13,20,16,10,20,25,17,19,14,19,14,18,22 %N A071915 Number of 1's in the continued fraction expansion of (3/2)^n. %C A071915 It seems that lim n ->infinity a(n)/n = 0.2... << (log(4)-log(3))/log(2) = 0.415... the expected density of 1's (cf. measure theory of continued fraction). %H A071915 Amiram Eldar, <a href="/A071915/b071915.txt">Table of n, a(n) for n = 1..10000</a> %e A071915 The continued fraction of (3/2)^24 is [16834, 8, 1, 10, 2, 25, 1, 3, 1, 1, 57, 6] which contains 4 "1's", hence a(24)=4. %t A071915 a[1] = 0; a[n_] := Count[ContinuedFraction[(3/2)^n], 1]; Array[a, 100] (* _Amiram Eldar_, Sep 05 2020 *) %o A071915 (PARI) for(n=1,200,s=contfrac(frac((3/2)^n)); print1(sum(i=1,length(s),if(1-component(s,i),0,1)),",")) %Y A071915 Cf. A071337, A071316, A071315, A071529. %K A071915 easy,nonn %O A071915 1,5 %A A071915 _Benoit Cloitre_, Jun 13 2002