[seqfan] Re: A209270 vs A083698

[Tomasz Ordowski]

Hans,

Note that 1 / [a(1);a(2),...,a(n)] = [0;a(1),a(2),...,a(n)].

Thomas

wt., 17 gru 2019 o 20:11 Hans Havermann <gladhobo at bell.net> napisał(a):

> I haven't seen any movement on this issue other than M.F. Hasler editing
> A209270 with a "same as A083698" crossref.
>
> I will point out that the Mathematica "Convergents" function of the
> initial terms yields {2, 3, 5/2, 13/5, 31/12, 137/53, 853/330, 6961/2693,
> 28697/11102, 179143/69305, ...}, so I can see that the numerators are in
> fact the prime terms of A072999 which (although A072999 isn't mentioned in
> A209270) reflects the wording of Benoit Cloitre's duplicate version.
>
> Paul Hanna's earlier A083698 has: "Partial quotients of the continued
> fraction which has convergents with the least possible prime denominators
> (A072999)." In light of the aforementioned convergents list, I am not
> really understanding this. Is this simply a case of the word "denominators"
> being incorrect?
>
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