Talk:Metallic ratios: Difference between revisions
Question the initial values for the "Lucas sequences"
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: Why is it that you call my 10,000 decimal digit example (REXX) an insane precision, but 1,000,000 was extremely precise? In any case, it has been deleted. But, my reason wasn't to see extremely precisely calculated values of phi. -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 01:30, 2 November 2019 (UTC)
== Initial values for the "Lucas sequences" ==
The initial values (1, 1) do not give the actual [https://en.wikipedia.org/wiki/Lucas_sequence Lucas sequences] used in mathematics. The Lucas sequences U_n(P,Q) and V_n(P,Q) are defined with the following initial values: U_0(P,Q) = 0, U_1(P,Q) = 1, and V_0(P,Q) = 2, V_1(P,Q) = P.
For example, [https://oeis.org/A006190 A006190](n) = U_n(3, -1), which, by definition, has the property that the ratio between successive terms converges to the bronze ratio.
On the other hand, there is no mentioning of "Lucas" or "bronze" in [https://oeis.org/A003688 A003688].
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