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Completing a dyadic sum
Suppose I knew the behaviour of a given sum in every other interval, for example:
$$
\sum_{\substack{0\leq a \leq x\\ a\equiv 1 (k)}} \sum_{x/(a+k/2)< b \leq x/a} f(b) \sim g(x),
$$
for any $x>1$...
-1
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1
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Taming this Conway-type sequence
(I started working on this problem after trying to get any "interesting" pattern out of the number that Gowers randomly wrote while answering:What is realistic mathematics?.)
The number was ...