bibkey: murthy2003a081459 authors: Amarnath Murthy; Artur Jasinski; Ehren Metcalfe year: 2003 title: OEIS A081459, numerators in the Newton iteration for the square root of five doi: null url: https://oeis.org/A081459 claim: A081459 records a(n+1) = 2a(n)^2 - 1 for n greater than one and a(n) = Lucas(32^(n-1))/2. strata_touched: [] license: citation-only triage: anchor

A081459 Newton–Pell numerators

Claim and scope

OEIS A081459 was authored by Amarnath Murthy on 2003-03-22. Artur Jasinski recorded the recurrence a(n+1)=2*a(n)^2-1 on 2008-10-12, and Ehren Metcalfe recorded a(n)=Lucas(3*2^(n-1))/2 on 2017-10-05. Consequently A081459(k+2) begins 9, 161, 51841, 5374978561, ... and is the layer sequence for the indices 6*2^k, for every integer k >= 0.