%I
%S 1,2,5,9,9,13,26,63,68,68,68,87,121,121,165,207,207,221,221,287,289,
%T 325,428,440,483,544,544,544,544,544,558,558,558,966,1035,1035,1146,
%U 1146,1332,1332,1332,1665,1665,1665,1665,1665,1727,1727,2052,2157,2331,2331
%N Least number k such that the continued fraction expansion of H(k) contains the numbers 1, 2, ..., n, where H(k) is the kth Harmonic number.
%H Charles R Greathouse IV, <a href="/A091656/b091656.txt">Table of n, a(n) for n = 1..250</a>
%e a(6) = 13 because CF( H(13)) = 3 + [5, 1, 1, 4, 2, 1, 3, 2, 1, 3, 1, 4, 1, 6], the first six integers are present.
%t f[n_] := Block[{k = 1}, While[ StringPosition[ ToString[ Union[ ContinuedFraction[ Sum[1/i, {i, 1, k}]]]], StringDrop[ ToString[ Table[i, {i, n}]], 1]] == {}, k++ ]; k]; Table[ f[n], {n, 1, 52}]
%o (PARI) list(lim)=my(v=vector(lim\1),n,t,H,i=1);while(1,H+=1/n++;t=vecsort(contfrac(H),,8);if(#t>=i&&t[i]==i,v[i]=n;print1(n":"i", ");if(i++>#v,return(v));H=1/n;n)) \\ _Charles R Greathouse IV_, Jan 25 2012
%Y Cf. A055573, A091655.
%K nonn
%O 1,2
%A _Robert G. Wilson v_, Jan 26 2004
