[seqfan] Little puzzle

David Wilson davidwwilson at comcast.net
Tue Apr 10 23:57:22 CEST 2018


Let r(k) = [k + 1/2] = k rounded to the nearest integer.

For integer n >= 0, define the sequence

S(k) = { r(k/2^n) : n  >= 1 }

So, for example, we have

f(11) = (r(11/2), r(11/4), r(11/8), ...) = (6, 3, 1, 1, 0, 0, 0, ...)

What are

SUM(k = 1..inf, f(k))
SUM(k = 1..inf, 2^k f(k)^2)




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