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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
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..250

EXAMPLE

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.

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}]

PROG

(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

CROSSREFS

Cf. A055573, A091655.

Sequence in context: A129140 A002580 A196408 * A273044 A133508 A125969

Adjacent sequences:  A091653 A091654 A091655 * A091657 A091658 A091659

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Jan 26 2004

STATUS

approved

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Last modified September 20 18:29 EDT 2021. Contains 347588 sequences. (Running on oeis4.)