A362602 Integers in the interval [Pi*k - 1/k, Pi*k + 1/k] for some k > 0 that are numerators of convergents to 2*Pi.

6, 19, 44, 333, 710, 103993, 312689, 2292816, 4272943, 10838702, 80143857, 411557987, 2549491779, 14885392687, 42106686282, 1783366216531, 8958937768937, 288469374822515, 856449186698608, 5706674932067741, 12269799050834090, 30246273033735921, 133254891185777774

Offset

1,1

Comments

Conjecture: the sequence is infinite.

Links

Table of n, a(n) for n=1..23.

Mathematica

hmax=30; A046955=Join[{1}, Numerator[Convergents[2Pi, hmax]]]; a={}; For[h=2, h<=hmax, h++, k=Intersection[List[Floor[Last[x/.N[Solve[Pi*x^2 - 1 - Part[A046955, h] x == 0, x], 2*hmax]]]], List[Ceiling[Last[x/.N[Solve[Pi*x^2 + 1 - Part[A046955, h] x == 0, x], 2*hmax]]]]]; If[k!={} && Ceiling[k*Pi - 1/k] == Floor[k*Pi + 1/k], AppendTo[a, Part[A046955, h]]]]; a

Crossrefs

Intersection of A046955 and A265735.

Sequence in context: A209403 A272707 A266938 * A299265 A005712 A299278

Adjacent sequences: A362599 A362600 A362601 * A362603 A362604 A362605

Keyword

nonn

Author

Alexander R. Povolotsky and Stefano Spezia, Apr 27 2023

Status

approved