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Greatest inverse of A071542, i.e., a(n) = maximal i such that A071542(i) = n.
10

%I #26 Dec 18 2016 12:54:09

%S 0,1,3,5,7,9,11,15,17,19,23,27,31,33,35,39,43,47,51,55,59,63,65,67,71,

%T 75,79,83,87,91,95,99,103,107,111,115,119,125,127,129,131,135,139,143,

%U 147,151,155,159,163,167,171,175,179,183,189,191,195,199,203,207

%N Greatest inverse of A071542, i.e., a(n) = maximal i such that A071542(i) = n.

%C What is s = lim sup a(n)/(n log_2(n))? A counting argument suggests s >= 1/2, and in any case s <= 1.

%C Essentially also the partial sums of A086876. - _Antti Karttunen_, Nov 10 2012 (per personal mail from _Carl R. White_, Nov 02 2012)

%H Charles R Greathouse IV and Antti Karttunen, <a href="/A173601/b173601.txt">Table of n, a(n) for n = 0..10000</a> (terms 1-10000 from Greathouse, Karttunen recomputed with prepended a(0)=0)

%F a(n)/log_2(a(n)) < n < a(n) for n > 1.

%o (PARI) v=vectorsmall(10^3);v[1]=1;for(n=2,#v,v[n]=v[n-hammingweight(n)]+1); u=vector(solve(x=1,#v,x*log(x)/log(2)-#v)\1);for(i=1,#v,if(v[i]<=#u,u[v[i]]=i)); u

%o (Scheme with Antti Karttunen's intseq-library): (define A173601 (PARTIALSUMS 1 0 (compose-funs A086876 1+)))

%Y See A213708 for the least inverse. A086876 gives the first differences. Also, a(n)=A213708(n)+A086876(n)-1. Cf. A071542, A179016, A218604, A218608.

%K nonn

%O 0,3

%A _Charles R Greathouse IV_, Oct 30 2012

%E Changed the starting offset by prepending a(0)=0 (with the indexing of the rest of terms thus not changed) - _Antti Karttunen_, Nov 10 2012