perplexus.info :: Sequences : Seven

Seven (Posted on 2021-08-15)

1, 7, 8, 49, 50…
The above sequence consists of positive integers each being a sum of distinct non-negative integer powers of 7 presented in strictly increasing order.

If a(0)=1 and a(1)=7, what is a(111)?

No Solution Yet Submitted by Ady TZIDON

Rating: 5.0000 (1 votes)

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Solution

| Comment 1 of 2

The simplest way is to convert to binary, but we need an offset of 1.

a(0)=1 = 7^0

a(1)=7 = 7^1

a(2)=8 = 7^1 + 7^0 but 2 in binary is 10 not 11 which is 3.

So for a(111) we need 112 in binary which is 1110000

a(111)=7^6+7^5+7^4=136857

Posted by Jer on 2021-08-16 09:31:59

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