A325158 Numerators of convergents to Pi using best rational approximation whose denominator is between consecutive powers of 2: [2^n, 2^(n+1)-1], where n = 0, 1, 2, ...
3, 6, 22, 44, 66, 179, 355, 710, 1065, 1775, 3550, 6745, 13135, 25915, 102928, 104348, 312689, 625378, 1146408, 3126535, 5419351, 10838702, 16258053, 47627751, 80143857, 165707065, 411557987, 657408909, 1068966896, 2549491779, 6167950454, 12335900908, 21053343141, 42106686282
Offset: 0
Keywords
Examples
The convergents are 3/1, 6/2, 22/7, 44/14, 66/21, 179/57, 355/113, 710/226, 1065/339, 1775/565, 3550/1130, 6745/2147, 13135/4181, 25915/8249, 102928/32763, ... = A325158/A325159.
Links
- Serguei Zolotov, Table of n, a(n) for n = 0..1023
- E. Charrier and L. Buzer, Approximating a real number by a rational number with a limited denominator: A geometric approach, Discrete Applied Mathematics, Volume 157, Issue 16, 28 August 2009, Pages 3473-3484.
- Serguei Zolotov, Python program to calculate b-file