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A071012 a(1)=1, a(n) is the smallest number >= a(n-1) such that the simple continued fraction for S(n) = 1/a(1) + 1/a(2) + ... + 1/a(n) contains exactly n elements. 2
1, 2, 3, 11, 16, 21, 27, 35, 42, 51, 55, 63, 75, 89, 350, 364, 385, 385, 416, 450, 453, 468, 476, 483, 526, 604, 617, 780, 1125, 1157, 1263, 1935, 7000, 7028, 7774, 8928, 9378, 62628, 865117, 17731648 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..40.

EXAMPLE

The continued fraction for S(6) = 1+1/2+1/3+1/11+1/16+1/21 is [2, 29, 9, 1, 3, 3] which contains 6 elements. The continued fraction for 1+1/2+1/3+1/11+1/16+1/21+1/27 is [2, 14, 169, 1, 1, 1, 4] which contains 7 elements and 27 is the smallest number >21 with this property, hence a(7) = 27.

MATHEMATICA

seq[len_] := Module[{s = {}, sum = 1, t = 1}, Do[sum += 1/t; While[Length[ContinuedFraction[sum + 1/t]] != n, t++]; AppendTo[s, t], {n, 1, len}]; s]; seq[39] (* Amiram Eldar, Jun 05 2022 *)

PROG

(PARI) s=1; t=1; for(n=1, 38, s=s+1/t; while(abs(n-length(contfrac(s+1/t)))>0, t++); print1(t, ", "))

CROSSREFS

Cf. A201267, A354742.

Sequence in context: A144979 A194558 A076514 * A354742 A228520 A280969

Adjacent sequences:  A071009 A071010 A071011 * A071013 A071014 A071015

KEYWORD

nonn,more

AUTHOR

Benoit Cloitre, May 19 2002

EXTENSIONS

One more term from Thomas Baruchel, Nov 16 2003

Name corrected and a(40) added by Amiram Eldar, Jun 05 2022

STATUS

approved

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Last modified August 14 06:54 EDT 2022. Contains 356110 sequences. (Running on oeis4.)