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 A316343 Concatenation of S[1], S[2], S[3], ..., where S[k] = 0 followed by m 1's, where m = (v+1)^2, v = exponent of highest power of 2 dividing k. 23
 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0 COMMENTS A word that is morphic and recurrent, but neither pure morphic, uniform morphic, primitive morphic, nor uniformly recurrent. LINKS Jack W Grahl, Table of n, a(n) for n = 0..999 Jean-Paul Allouche, Julien Cassaigne, Jeffrey Shallit, Luca Q. Zamboni, A Taxonomy of Morphic Sequences, arXiv preprint arXiv:1711.10807 [cs.FL], Nov 29 2017. EXAMPLE S[4] = 0,1,1,1,1,1,1,1,1,1. MATHEMATICA S[k_] := Join[{0}, Table[1, {(IntegerExponent[k, 2] + 1)^2}]]; Array[S, 20] // Flatten (* Jean-François Alcover, Nov 02 2018 *) PROG (Haskell) a316343_count :: Integer -> Int a316343_count n = fromIntegral ((v + 1) ^ 2) where     v         | n `mod` 2 == 1 = 0         | otherwise      = 1 + (n `div` 2) a316343_S :: Integer -> [Integer] a316343_S n = 0 : (replicate (a316343_count n) 1) a316343 :: [Integer] a316343 = concatMap a316343_S [1..] -- Jack W Grahl, Jul 23 2018 CROSSREFS Sequences mentioned in the Allouche et al. "Taxonomy" paper, listed by example number: 1: A003849, 2: A010060, 3: A010056, 4: A020985 and A020987, 5: A191818, 6: A316340 and A273129, 18: A316341, 19: A030302, 20: A063438, 21: A316342, 22: A316343, 23: A003849 minus its first term, 24: A316344, 25: A316345 and A316824, 26: A020985 and A020987, 27: A316825, 28: A159689, 29: A049320, 30: A003849, 31: A316826, 32: A316827, 33: A316828, 34: A316344, 35: A043529, 36: A316829, 37: A010060. Sequence in context: A277674 A309754 A112690 * A288864 A115971 A320007 Adjacent sequences:  A316340 A316341 A316342 * A316344 A316345 A316346 KEYWORD nonn AUTHOR N. J. A. Sloane, Jul 14 2018 EXTENSIONS More terms from Jack W Grahl, Jul 23 2018 STATUS approved

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Last modified July 28 23:26 EDT 2021. Contains 346340 sequences. (Running on oeis4.)