The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

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