Highest Power of 2 Dividing Numerator of Sum of Odd Reciprocals/Historical Note

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Historical Note on Highest Power of 2 Dividing Numerator of Sum of Odd Reciprocals

This result was posed as an elementary problem by John Lewis Selfridge in March $1960$: Problems for Solution: E1406-E1410 (American Mathematical Monthly Vol. 67: 290)  www.jstor.org/stable/2309704.

He notes that H.S. Shapiro and D.L. Slotnick leave the problem unsolved in an article in a $1959$ commercial publication, where they suggest that:

an estimate [of this] power of $2$ ... seems in general to be a difficult number theoretic problem.


In the event, $7$ contributors are reported as having submitted a solution, of which that by D.L. Silverman was the one published.


Among the solvers was Donald E. Knuth, who included the problem as an exercise of difficulty level $M33$ in his The Art of Computer Programming: Volume 1: Fundamental Algorithms.


Sources