Talk:Metallic ratios: Difference between revisions
→Initial values for the "Lucas sequences": Maybe Lucas-like sequences?
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Thundergnat (talk | contribs) (→Initial values for the "Lucas sequences": Maybe Lucas-like sequences?) |
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On the other hand, there is no mentioning of "Lucas" or "bronze" in [https://oeis.org/A003688 A003688]. See also the Sidef entry, which uses the actual Lucas sequences. -- [[User:Trizen|Trizen]] ([[User talk:Trizen|talk]]) 13:02, 2 November 2019 (UTC)
:You aren't wrong, and perhaps I should specify more clearly that these are a ''variant'' of Lucas sequences in the task description (Lucas-like sequences?). Actual Lucas sequences are of the form
xₙ = P * xₙ₋₁ - Q * xₙ₋₂.
:and I glossed over the fact that the value I chose for c (Q) means we are subtracting -1 rather than adding +1 as it makes no difference to the answer. As for starting at 1 rather than 0... yeah, well, I mostly chose that to avoid the complication of having to trap divide by zero errors. The ratios work out due to the interval between terms; the starting value has very little effect. It may change how many terms it takes to converge (by at most 1), but the point I was trying to demonstrate with this task was the fact that the ratios ''could'' be calculated this way and the relative "''speed''" at which they converge not the actual number. --[[User:Thundergnat|Thundergnat]] ([[User talk:Thundergnat|talk]]) 13:06, 2 November 2019 (UTC)
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