A055114 Numbers k such that the continued fraction for m/k contains a term >= 3 for every 1 <= m < k.

23, 37, 53, 59, 61, 83, 103, 107, 113, 127, 137, 139, 149, 151, 197, 211, 223, 227, 229, 331, 347, 349, 353, 359, 383, 421, 439, 461, 479, 491, 509, 523, 529, 541, 557, 563, 569, 607, 631, 739, 751, 757, 761, 769, 797, 809, 811, 821, 823, 827, 829, 839, 851

Offset

1,1

Comments

Composite terms begin a(33) = 529, a(53) = 851, a(77) = 1357, .... - Charles R Greathouse IV, Mar 11 2014

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

23 is in sequence because continued fractions for 1/23, 2/23, ..., 22/23 each contain a term >= 3.

Mathematica

q[n_] := AllTrue[Range[1, n - 1], Max[ContinuedFraction[#/n]] > 2 &]; Select[Range[2, 1000], q] (* Amiram Eldar, Jun 25 2022 *)

Prog

(PARI) drop(v)=v[2..#v]
is(n)=for(k=1, n-1, if(vecmax(drop(contfrac(k/n)))<3, return(0))); n>1 \\ Charles R Greathouse IV, Mar 11 2014

Crossrefs

Cf. A082409.

Sequence in context: A209617 A179780 A153740 * A329262 A268343 A063643

Adjacent sequences: A055111 A055112 A055113 * A055115 A055116 A055117

Keyword

nonn

Author

David W. Wilson, Jun 16 2000

Status

approved