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A088023 Set a(1) = 1. Then take the list of defined initial terms, reverse their order, add 1, 2, 3...to the reversed list in succession, and append this new list to the right of the previously defined terms. Repeat this process indefinitely. +0
4
1, 2, 3, 3, 4, 5, 5, 5, 6, 7, 8, 8, 8, 9, 9, 9, 10, 11, 12, 12, 13, 14, 14, 14, 14, 15, 16, 16, 16, 17, 17, 17, 18, 19, 20, 20, 21, 22, 22, 22, 23, 24, 25, 25, 25, 26, 26, 26, 26, 27, 28, 28, 29, 30, 30, 30, 30, 31, 32, 32, 32, 33, 33, 33 (list; graph; listen)
OFFSET

1,2

COMMENT

Conjecture: a(n+1) >= a(n). Comments from Don Reble (djr(AT)nk.ca), Nov 13 2005: The conjecture is plainly true. In fact, a(n+1)-a(n) = 0 or 1. Also a(A091072(n)) = n; a(A091072(n)+1) = n+1.

FORMULA

a(n)=2a(n/2)-1 if a=2^k else a(n)=a(2^k-n+1)+n-2^(k-1) if 2^(k-1)<n<2^k. (Ed.)

EXAMPLE

The sequence begins 1, 2, then reverse 1, 2 = 2, 1 then add 1, 2 to the latter getting 3, 3. Then append 3, 3, to the right of 1, 2, getting 1, 2, 3, 3. Then repeating the instructions, 1, 2, 3, 3 is reversed then add 1, 2, 3, 4 to 3, 3, 2, 1, = 4, 5, 5, 5. Append the latter to 1, 2, 3, 3 getting 1, 2, 3, 3, 4, 5, 5, 5...; and so on.

CROSSREFS

Sequence in context: A075458 A083036 A073092 this_sequence A133316 A061451 A086155

Adjacent sequences: A088020 A088021 A088022 this_sequence A088024 A088025 A088026

KEYWORD

nonn

AUTHOR

Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 19 2003

EXTENSIONS

Edited by John W. Layman (layman(AT)math.vt.edu), Oct 10 2003

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Last modified July 26 13:41 EDT 2008. Contains 142293 sequences.


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