A089642 Numbers m such that there is a single k, 1 <= k <= m, such that the number of elements in the continued fraction for m/k is maximum.

1, 3, 4, 5, 8, 12, 13, 15, 21, 30, 34, 39, 40, 42, 48, 55, 56, 65, 72, 74, 80, 89, 102, 110, 130, 144, 168, 170, 176, 180, 185, 193, 194, 208, 233, 272, 275, 288, 297, 299, 312, 336, 340, 377, 400, 445, 456, 468, 517, 546, 550, 610, 638, 699, 715, 720, 754, 777

Offset: 1

Author

Benoit Cloitre, Jan 01 2004

Keywords

• nonn

Comments

Except for 2, all Fibonacci numbers are in the sequence.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..250

Crossrefs

Cf. A000045, A084242.

Programs

Mathematica

q[n_] := Count[len = Length[ContinuedFraction[n/#]] & /@ Range[n], Max[len]] == 1; Select[Range[1000], q] (* Amiram Eldar, Jun 14 2022 *)

PARI

for(n=1,330,if(sum(s=1,n,if(length(contfrac(n/s))-vecmax(vector(n,i,length(contfrac(n/i)))),0,1))==1,print1(n,",")))

Extensions

More terms from Jinyuan Wang, Apr 06 2020