

A071012


a(1)=1, a(n) is the smallest number >= a(n1) 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(nlength(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



