Binary Sequence Puzzle
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From: Leroy Quet on 28 May 2010 15:40 Leroy Quet wrote: By the way, here is the EIS entry. It has just appeared. (I have submitted the correction mentioned above, but that hasn't appeared yet as of now.) http://oeis.org/classic/A175480 Thanks, Leroy Quet
From: Leroy Quet on 28 May 2010 15:42 Ludovicus wrote: > On 28 mayo, 10:12, Leroy Quet <qqq...(a)mindspring.com> wrote: > > \ > > What rule best determines the pattern of 0's and 1's in this > > infinite sequence. > > As a Fourier Series can determine any pattern, you must to specify > what type of function is permissible. There are actually an infinite number of sequences that match mine in the starting terms. I know this. But try to find an *interesting* (subjective, I know) definition that fits. :) Thanks, Leroy Quet
From: James Dow Allen on 29 May 2010 02:10 On May 29, 12:35 am, Ludovicus <luir...(a)yahoo.com> wrote: > On 28 mayo, 10:12, Leroy Quet <qqq...(a)mindspring.com> wrote: > > What rule best determines the pattern of 0's and 1's in this > > infinite sequence. > . > As a Fourier Series can determine any pattern, you must to specify > what type of function is permissible. (Leroy mentioned this sort of objection in his OP.) One often hears similar objection to "Find the next number in this sequence" problems, but I think it's often misapplied. Clearly one seeks the *simplest* answer; i.e. a pattern which can be expressed with fewer words (or perhaps, since we're cross-posted to sci.math, less Kolmogorov complexity). Now *some* such puzzles may have two (or more) answers with almost equally simple explanations. But that would make them *more* fun, not less! Any examples? James
From: Leroy Quet on 29 May 2010 08:21 James Dow Allen wrote: /.... / Now *some* such puzzles may have two (or more) answers / with almost equally simple explanations. But that would / make them *more* fun, not less! Any examples? / Here are the sequences that start 2,3,5,7,11,13,17,19,23 in the EIS that do NOT contain the word prime anywhere in their entry: http://oeis.org/classic/?q=2%2C3%2C5%2C7%2C11%2C13%2C17%2C19%2C23++-prime&sort=0&fmt=0&language=english&go=Search Thanks, Leroy Quet
From: Leroy Quet on 29 May 2010 08:28
Leroy Quet wrote: > James Dow Allen wrote: > /.... > / Now *some* such puzzles may have two (or more) answers > / with almost equally simple explanations. But that would > / make them *more* fun, not less! Any examples? > / > > Here are the sequences that start > 2,3,5,7,11,13,17,19,23 > in the EIS that do NOT contain the word prime anywhere in their entry: > http://oeis.org/classic/?q=2%2C3%2C5%2C7%2C11%2C13%2C17%2C19%2C23++-prime&sort=0&fmt=0&language=english&go=Search > PS: The only really interesting example here is A005180, the orders of simple groups. This sequence contains the primes up to 59, then a 60. I also personally like A161578, one of my own. "a(1)=2. a(n) = the smallest integer > a(n-1) such that d(a(n)) <= d(n), where d(n) = the number of divisors of n." A 25 immediately follows the 23 in this sequence. Thanks, Leroy Quet |