bibkey: murthy2003a081460 authors: Amarnath Murthy; Ehren Metcalfe; Amiram Eldar year: 2003 title: OEIS A081460, denominators in the Newton iteration for the square root of five doi: null url: https://oeis.org/A081460 claim: A081460 records a(n) = F(3*2^(n-1))/2 and a Lucas-product formula for the same values. strata_touched: [] license: citation-only triage: anchor

A081460 Newton–Pell denominators

Claim and scope

OEIS A081460 was authored by Amarnath Murthy on 2003-03-22. Ehren Metcalfe recorded the formula a(n)=F(3*2^(n-1))/2 on 2017-10-07. Amiram Eldar recorded on 2023-04-07 the product

$$a(n)=\prod _{r=1}^{n-1}Lucas(3\cdot 2^{n-1-r}).$$

At n=k+2, these formulas give A081460(k+2)=F(6*2^k)/2; combined with A081459’s Lucas formula, the product gives F(6*2^k)=2^(k+3)*Product_{0<=j<k} A081459(j+2) for every integer k >= 0.