[seqfan] Re: Hofstadter-Conway $10,000 Sequence
David Wilson
davidwwilson at comcast.net
Tue Jul 7 23:59:43 CEST 2009
Compare
http://mathworld.wolfram.com/Hofstadter-Conway10000-DollarSequence.html
with
http://www.research.att.com/~njas/sequences/table?a=139250&fmt=5
----- Original Message -----
From: <franktaw at netscape.net>
To: <seqfan at seqfan.eu>
Sent: Tuesday, July 07, 2009 4:04 PM
Subject: [seqfan] Hofstadter-Conway $10,000 Sequence
>I just submitted a new sequence:
>
> %S A162598
> 1,1,2,1,3,4,2,1,5,6,7,3,8,4,2,1,9,10,11,12,5,13,14,6,15,7,3,16,8,4,2,1,
> %T A162598
> 17,18,19,20,21,9,22,23,24,10,25,26,11,27,12,5,28,29,13,30,14,6,31,15,7,
> %U A162598
> 3,32,16,8,4,2,1,33,34,35,36,37,38,17,39,40,41,42,18,43,44,45,19,46,47
> %N A162598 Ordinal transform of modified A051135.
> %C A162598 This is a fractal sequence.
> %C A162598 It appears that each group of 2^k terms starts with 1 and
> ends with the remaining powers of two from 2^k down to 2^1.
> %F A162598 Let b(1) = 1, b(n) = A051135(n) for n > 1. Then a(n) is the
> number of b(k) that equal b(n) for 1 <= k <= n: sum( 1, 1<=k<=n and
> a(k)=a(n) ).
> %Y A162598 Cf. A004001,A051135.
> %K A162598 nonn
> %O A162598 1,3
>
> The conjecture here might, if established, throw some light on the
> behavior of the Hofstadter-Conway $10,000 Sequence.
>
> (The ordinal transform is the transform specified by the second
> sentence in the formula line. As noted in A051135, the modified
> sequence here called b(n) is identical to its lower-trimmed
> subsequence; the ordinal transform of such a sequence is a fractal
> sequence, and vice versa.)
>
> Franklin T. Adams-Watters
>
>
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>
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