Some of the sequences being studied (like the example in the summary) use formulations developed from base 10 numbers. Have you explored other bases, in particular prime number bases, or perhaps a rational fraction or even irrational/transcendent number? If so, were there any interesting surprises?
That sequence is in the database as http://oeis.org/A047778 [oeis.org] since at least 1999.
Funny, just one month ago, Neil Sloan asked "the smallest prime in this sequence is 485398038695407. What is the full subsequence of primes?"
For the moment, the first is also the only prime known in this sequence.
I tought his sequence was listing all the numerical symbols sequentially, adding a digit each time, and repeating when all the symbols have been used. Thus having 1234567890123...etc...
Now I see that after 9 it's ten, eleven,twelve, etc...
So in binary it's indeed
1, 110, 11011, 11011100, etc...
Thanks!
"Those who will be able to conquer software will be able to conquer the
world."
-- Tadahiro Sekimoto, president, NEC Corp.
Base 10 sequences, other bases of interest? (Score:5, Interesting)
Some of the sequences being studied (like the example in the summary) use formulations developed from base 10 numbers. Have you explored other bases, in particular prime number bases, or perhaps a rational fraction or even irrational/transcendent number? If so, were there any interesting surprises?
Re: (Score:2)
I just tried his sequence but in base 2 (since I'm a programmer!)
1, 10, 101, 1010, 10101, 101010, etc...
The pattern is boring, each binary value in the sequence, when converted in decimal, repeats the following:
previous value x 2
previous value x 2 + 1
The same list in decimal:
1, 2, 5, 10, 21, 42, etc...
Re: (Score:2)
Re: (Score:2)
Yes I'm a good programmer, I work in assembly you insensitive clod!
Like I did mention in my reply, I read the summary too fast, and tought that it was another sequence.
Well, it turns out that the sequence I was thinking about exists: https://oeis.org/A057137/ [oeis.org]
There! :-p
Re: (Score:1)
Re: (Score:2)
Yes, I see my error.
I tought his sequence was listing all the numerical symbols sequentially, adding a digit each time, and repeating when all the symbols have been used. Thus having 1234567890123...etc...
Now I see that after 9 it's ten, eleven ,twelve, etc...
So in binary it's indeed
1, 110, 11011, 11011100, etc...
Thanks!