

A088748


a(n) = 1 + sum(k=0 to n1) [2 * A014577(k)  1].


4



1, 2, 3, 2, 3, 4, 3, 2, 3, 4, 5, 4, 3, 4, 3, 2, 3, 4, 5, 4, 5, 6, 5, 4, 3, 4, 5, 4, 3, 4, 3, 2, 3, 4, 5, 4, 5, 6, 5, 4, 5, 6, 7, 6, 5, 6, 5, 4, 3, 4, 5, 4, 5, 6, 5, 4, 3, 4, 5, 4, 3, 4, 3, 2, 3, 4, 5, 4, 5, 6, 5, 4, 5, 6, 7, 6, 5, 6, 5, 4, 5, 6, 7, 6, 7, 8, 7, 6, 5, 6, 7, 6, 5, 6, 5, 4, 3, 4, 5, 4, 5, 6
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OFFSET

0,2


COMMENTS

Let s(0)=1; s(n+1)=s(n),ri(n), where ri(n) is s(n) reversed and incremented. Each s(n) is an initial part of this sequence.
For each m, a(1 to 2^m) is a permutation of A063787(1 to 2^m). For k=1 to 2^m, a(2^m+1A088372(m,k)) = A063787(k).
Partial sums of the sequence = A164910: (1, 3, 6, 8, 11, 15, 20,...).
a(0) = 1, then using the dragon curve sequence A014577: (1, 1, 0, 1, 1,...) as a code: (1 = add to current term, 0 = subtract from current term, to get the next term), see example.
Rows of A088696 tend to this sequence..


LINKS

Table of n, a(n) for n=0..101.


FORMULA

a(n) = 1 + A005811(n). [Joerg Arndt, Dec 11 2012]


EXAMPLE

The first 8 terms of the sequence = (1, 2, 3, 2, 3, 4, 3, 2), where the first
four terms = (1, 2, 3, 2). Reverse, add 1, getting (3, 4, 3, 2), then append.
The sequence begins with "1", then using the dragon curve coding, we get:
1...2...3...2...3...4... = A088748
....1...1...0...1...1... = A014577, the dragon curve.


CROSSREFS

Cf. A014577, A063787, A088208, A088372, A088696.
Sequence in context: A106383 A175794 A105500 * A086374 A123182 A069464
Adjacent sequences: A088745 A088746 A088747 * A088749 A088750 A088751


KEYWORD

nonn


AUTHOR

Gary W. Adamson, Oct 14 2003


EXTENSIONS

Edited by Don Reble (djr(AT)nk.ca), Nov 15 2005
Additional comments from Gary W. Adamson, Aug 30 2009
Edited by N. J. A. Sloane, Sep 06 2009


STATUS

approved



