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.
1, 2, 5, 9, 9, 13, 26, 63, 68, 68, 68, 87, 121, 121, 165, 207, 207, 221, 221, 287, 289, 325, 428, 440, 483, 544, 544, 544, 544, 544, 558, 558, 558, 966, 1035, 1035, 1146, 1146, 1332, 1332, 1332, 1665, 1665, 1665, 1665, 1665, 1727, 1727, 2052, 2157, 2331, 2331
Offset: 1
Keywords
Examples
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.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..250
Programs
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Mathematica
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}] -
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