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Sum of distinct powers of 7

Source: PRMO 2019 leg 2 P13

August 25, 2019
OEISPRMOnumber theory

Problem Statement

Consider the sequence 1,7,8,49,50,56,57,343…1,7,8,49,50,56,57,343\ldots which consists of sums of distinct powers of77, that is, 707^0, 717^1, 70+717^0+7^1, 727^2,…\ldots in increasing order. At what position will 1685616856 occur in this sequence?
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