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A091656 Least number k such that the continued fraction expansion of H(k) contains the numbers 1, 2, ..., n, where H(k) is the k-th Harmonic number. 2

%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 k-th 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

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Last modified October 27 13:45 EDT 2021. Contains 348276 sequences. (Running on oeis4.)