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 A181935 Curling number of binary expansion of n. 8
 1, 1, 1, 2, 2, 1, 1, 3, 3, 1, 2, 2, 2, 1, 1, 4, 4, 1, 1, 2, 2, 2, 1, 3, 3, 1, 2, 2, 2, 1, 1, 5, 5, 1, 1, 2, 2, 2, 1, 3, 3, 1, 3, 2, 2, 2, 1, 4, 4, 1, 1, 2, 2, 2, 2, 3, 3, 1, 2, 2, 2, 1, 1, 6, 6, 1, 1, 2, 2, 2, 1, 3, 3, 2, 2, 2, 2, 1, 1, 4, 4, 1, 2, 2, 2, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Given a string S, write it as S = XYY...Y = XY^k, where X may be empty, and k is as large as possible; then k is the curling number of S. A212439(n) = 2 * n + a(n) mod 2. - Reinhard Zumkeller, May 17 2012 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..8191 Benjamin Chaffin and N. J. A. Sloane, The Curling Number Conjecture, preprint. EXAMPLE 731 = 1011011011 in binary, which we could write as XY^2 with X = 10110110 and Y = 1, or as XY^3 with X = 1 and Y = 011. The latter is better, giving k = 3, so a(713) = 3. PROG (Haskell) import Data.List (unfoldr, inits, tails, stripPrefix) import Data.Maybe (fromJust) a181935 0 = 1 a181935 n = curling \$ unfoldr    (\x -> if x == 0 then Nothing else Just \$ swap \$ divMod x 2) n where    curling zs = maximum \$ zipWith (\xs ys -> strip 1 xs ys)                           (tail \$ inits zs) (tail \$ tails zs) where       strip i us vs | vs' == Nothing = i                     | otherwise      = strip (i + 1) us \$ fromJust vs'                     where vs' = stripPrefix us vs -- Reinhard Zumkeller, May 16 2012 CROSSREFS Cf. A212412 (parity), A212440, A212441, A007088, A090822, A224764/A224765 (fractional curling number). Sequence in context: A037162 A278566 A255559 * A027358 A332548 A191781 Adjacent sequences:  A181932 A181933 A181934 * A181936 A181937 A181938 KEYWORD nonn,base AUTHOR N. J. A. Sloane, Apr 02 2012 STATUS approved

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Last modified May 6 07:01 EDT 2021. Contains 343580 sequences. (Running on oeis4.)