The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A177045 The ordering of expressions built from numbers 2 and exponentiations according to their numeric values. 0
1, 2, 3, 4, 7, 8, 9, 5, 6, 17, 18, 21, 22, 23, 15, 16, 19, 20, 49, 50, 51, 59, 60, 63, 64, 65, 43, 44, 45, 46, 47, 48, 57, 58, 61, 62, 149, 150, 153, 154, 155, 181, 182, 183, 191, 192, 195, 196, 197, 136, 137, 138, 139, 140, 141, 147, 148, 151, 152, 175, 176, 177, 178, 179, 180, 189, 190, 193, 194, 478, 479, 480, 488, 489, 492, 493, 494, 578, 579, 582, 583, 584, 610, 611, 612, 620, 621, 624, 625, 626, 12, 13, 14, 132, 133, 134, 135, 439, 440, 441 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Let S be the sequence of all possible expressions built from numbers 2 and exponentiations (^), sorted according to their natural structural ordering (2, 2^2, 2^(2^2), (2^2)^2, 2^(2^(2^2)), 2^((2^2)^2) and so on - see the exact definition in Haskell below).
Let S' be S stable-sorted according to the numeric values of its elements in ascending order (the stable sorting is a sorting that keeps the order of elements with equal keys - so 2^(2^2) and (2^2)^2 will be kept in the original order).
This sequence is S' where each expression is replaced with its original index (1-based) in S; it is a permutation of the natural numbers sequence.
LINKS
PROG
(Haskell) data Expr = Two | Expr :^: Expr
-- needed only for presentation
instance Show Expr where show Two = "2"; show (x :^: y) = "(" ++ show x ++ "^" ++ show y ++ ")"
ofSize 1 = [Two]
ofSize n = [left :^: right | k <- [1..n-1], left <- ofSize k, right <- ofSize (n-k)]
-- this defines the S sequence
s = [e | n <- [1..], e <- ofSize n]
CROSSREFS
Sequence in context: A297164 A207800 A109436 * A241783 A039254 A039195
KEYWORD
nonn
AUTHOR
EXTENSIONS
First 100 terms from D. S. McNeil, May 04 2010
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 19 20:45 EDT 2024. Contains 372703 sequences. (Running on oeis4.)