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.

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

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 A361127

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