[seqfan] Hofstadter-Conway $10,000 Sequence
franktaw at netscape.net
franktaw at netscape.net
Tue Jul 7 22:04:53 CEST 2009
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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