A354742 a(1)=1, a(n) is the smallest number > a(n-1) such that the simple continued fraction for 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, 536, 644, 707, 4290, 10483, 13818, 2923344, 3187100, 7820430, 31734729, 39111981

Offset

1,2

Links

Table of n, a(n) for n=1..28.

Mathematica

seq[len_] := Module[{s = {}, sum = 0, t = 0}, Do[t++; While[Length[ContinuedFraction[sum + 1/t]] != n, t++]; sum += 1/t; AppendTo[s, t], {n, 1, len}]; s]; seq[23]

Prog

(PARI) s=0; t=0; for(n=1, 40, t++; while(length(contfrac(s+1/t)) != n, t++); s+=1/t; print1(t, ", "))

Crossrefs

Cf. A071012, A201267.

Sequence in context: A194558 A076514 A071012 * A228520 A361127 A280969

Adjacent sequences: A354739 A354740 A354741 * A354743 A354744 A354745

Keyword

nonn,more

Author

Amiram Eldar, Jun 05 2022

Status

approved