Abstract
We evaluate some unusual infinite products, of which the following is a typical example: 3 −1 3 = 1 2 · 6 4 · 8 9 · 12 10 · 14 15 · 16 17 · 20 21 · 22 23 · 27 25 … . Here the numbers n in the denominator are { n: s 3( n − 1) ≡ 0 (mod 3)} and the numbers d in the denominator are { d: s 3( d − 1) ≡ 1(mod 3)}, where s k ( n) denotes the sum of the digits of n when expressed in base k.
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