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Let $n=(a_ka_{k-1}\ldots a_1a_0)_2$. Then the $n$-th number in the sequence is $3^ka_k+3^{k-1}a_{k-1}\cdots+3^1a_1+a_0$. It hinges on the fact that $3^{r+1}>1+3+\cdots+3^r$. Therefore the 100th number is $3^6+3^5+3^2$.

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Hi caffeinemachine, thanks for participating in the problem and your answer is correct.Let $n=(a_ka_{k-1}\ldots a_1a_0)_2$. Then the $n$-th number in the sequence is $3^ka_k+3^{k-1}a_{k-1}\cdots+3^1a_1+a_0$. It hinges on the fact that $3^{r+1}>1+3+\cdots+3^r$. Therefore the 100th number is $3^6+3^5+3^2$.

I want also to say that at MHB, we are never short of talented maths experts here, and I've gained some very useful insights from the site, and for this I am so thankful!

- Mar 10, 2012

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Keep such problems coming anemone!Hi caffeinemachine, thanks for participating in the problem and your answer is correct.

I want also to say that at MHB, we are never short of talented maths experts here, and I've gained some very useful insights from the site, and for this I am so thankful!

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Hey caffeinemachine, are you one of the ardent fans of sequences and series?Keep such problems coming anemone!

- Mar 10, 2012

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Not really.. In the olympiad genre I am an 'ardent fan' of Combinatorics and Geometry questions. In curriculum mathematics I like Discrete math the most, esp Algebra and Combinatorics. And among the mathematical disciplines in which I am a newbie I find Relativity and Non Euclidean Geometry the most fascinating and Romantic.Hey caffeinemachine, are you one of the ardent fans of sequences and series?

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How about you? Your math interests?Hey caffeinemachine, are you one of the ardent fans of sequences and series?

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I see...Not really.. In the olympiad genre I am an 'ardent fan' of Combinatorics and Geometry questions. In curriculum mathematics I like Discrete math the most, esp Algebra and Combinatorics. And among the mathematical disciplines in which I am a newbie I find Relativity and Non Euclidean Geometry the most fascinating and Romantic.

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How about you? Your math interests?

For me, my interests lie in trigonometry and sequences and series, which I think is a shameful thing to just like mathematics in these two narrow fields of mathematics...