Think "Twice"

Let S\large S be the set of all integers of the form 2a+2b+2c\large 2^{a}+2^{b}+2^{c}, where a,b,c\large a, b, c are mutually distinct whole numbers.

When all the elements of S\large S are arranged in ascending order, find the 100th\large 100^{th} element.

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