A325159 Denominators 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, ...
1, 2, 7, 14, 21, 57, 113, 226, 339, 565, 1130, 2147, 4181, 8249, 32763, 33215, 99532, 199064, 364913, 995207, 1725033, 3450066, 5175099, 15160384, 25510582, 52746197, 131002976, 209259755, 340262731, 811528438, 1963319607, 3926639214, 6701487259, 13402974518, 20104461777
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