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The Millin series is defined as:

$$\sum_{n \mathop = 0}^\infty \frac 1 {F_{2^n} }$$

where $F_n$ denotes the $n$th Fibonacci number.

It can be shown to equal $\dfrac {7 - \sqrt 5} 2$.

But who was the D.A. Millin who it is named after?

EDIT: User https://hsm.stackexchange.com/users/16591/michael has located the issue of FQ in which Millin's name originally appears, where he was identified as a Pennsylvanian high-school student in 1974.

Further to this, I have found that the solution appeared in FQ issue Vol. 14 no. 2 (1976), but in this case his name appears as D.A. Miller.

The question arises as to whether Millin might have been a misprint. If his name truly is "Miller", then his precise identity may be very difficult to track down. There is a professor in Virginia with that name, but he appears a couple of decades too young.

Whoever he is, he may well be currently active.

Prime Mover
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2 Answers2

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I am the author of the Advanced Problem H-237 to the FQ issue Vol. 14 no. 2 (1976). The series in that Problem was later named the Millin series. At that time, I was a senior at the Annville-Cleona High School in Pennsylvania. This series was also part of the paper titled "Observations in Pure Mathematics" that I submitted to the 1974 Westinghouse Science Talent Search (now the Regeneron Science Talent Search). In the days before LaTeX, I wrote my submission to FQ using a combination of handwriting and a typewriter. Apparently, my handwritten signature was not clear and was misread at the time.

Frankly, I like the name "the Millin Series," and I hope no one makes an effort to change it. For my proof of this identity, see the last entry on this webpage

Dale A Miller, Research Scientist, Inria, France

Dale Miller
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The furthest back I came is this 1974 article from The Fibonacci Quarterly 12, No. 3.

Extract: enter image description here

Michael
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