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 A252867 a(n) = n if n <= 2, otherwise the smallest number not occurring earlier having in its binary representation at least one bit in common with a(n-2), but none with a(n-1). 18
 0, 1, 2, 5, 10, 4, 3, 12, 17, 6, 9, 18, 8, 7, 24, 33, 14, 32, 11, 36, 19, 40, 16, 13, 48, 15, 80, 34, 20, 35, 28, 65, 22, 41, 66, 21, 42, 68, 25, 38, 72, 23, 64, 26, 69, 50, 73, 52, 67, 44, 81, 46, 129, 30, 97, 130, 29, 98, 132, 27, 100, 131, 56, 70, 49, 74, 37, 82 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Conjectured to be a permutation of the nonnegative integers. [Comment modified by N. J. A. Sloane, Jan 10 2015] This is a purely set-based version of A098550, using the binary representation of numbers. LINKS Chai Wah Wu, Table of n, a(n) for n = 0..50002 (First 10000 terms from Reinhard Zumkeller) David L. Applegate, Hans Havermann, Bob Selcoe, Vladimir Shevelev, N. J. A. Sloane, and Reinhard Zumkeller, The Yellowstone Permutation, arXiv preprint arXiv:1501.01669, 2015 and J. Int. Seq. 18 (2015) 15.6.7. Chai Wah Wu, Scatterplot of first million terms Chai Wah Wu, Scatterplot of first million terms, with red lines powers of 2. Chai Wah Wu, Gzipped file with first million terms [Save file, delete .txt suffix, then open] EXAMPLE The sequence of sets is {}, {0}, {1}, {0,2}, {1,3}, {2}, {0,1}, {3,4}. After the initial 3 terms, a(n) is the minimum set (as ordered by A048793) that has a nonempty intersection with a(n-2) but empty intersection with a(n-1). Comment from N. J. A. Sloane, Dec 31 2014: The binary expansions of the first few terms are: 0  = 000000 1  = 000001 2  = 000010 5  = 000101 10 = 001010 4  = 000100 3  = 000011 12 = 001100 17 = 010001 6  = 000110 9  = 001001 18 = 010010 8  = 001000 7  = 000111 24 = 011000 33 = 100001 14 = 001110 32 = 100000 11 = 001011 36 = 100100 19 = 010011 40 = 101000 ... MATHEMATICA a[n_] := a[n] = If[n<3, n, For[k=3, True, k++, If[FreeQ[Array[a, n-1], k], If[BitAnd[k, a[n-2]] >= 1 && BitAnd[k, a[n-1]] == 0, Return[k]]]]]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Oct 03 2018 *) PROG (PARI) invecn(v, k, x)=for(i=1, k, if(v[i]==x, return(i))); 0 alist(n)=local(v=vector(n, i, i-1), x); for(k=4, n, x=3; while(invecn(v, k-1, x)||!bitand(v[k-2], x)||bitand(v[k-1], x), x++); v[k]=x); v (Haskell) import Data.Bits ((.&.)); import Data.List (delete) a252867 n = a252867_list !! n a252867_list = 0 : 1 : 2 : f 1 2 [3..] where    f :: Int -> Int -> [Int] -> [Int]    f u v ws = g ws where      g (x:xs) = if x .&. u > 0 && x .&. v == 0                    then x : f v x (delete x ws) else g xs -- Reinhard Zumkeller, Dec 24 2014 (Python) A252867_list, l1, l2, s, b = [0, 1, 2], 2, 1, 3, set() for _ in range(10**2): ....i = s ....while True: ........if not (i in b or i & l1) and i & l2: ............A252867_list.append(i) ............l2, l1 = l1, i ............b.add(i) ............while s in b: ................b.remove(s) ................s += 1 ............break ........i += 1 # Chai Wah Wu, Dec 27 2014 CROSSREFS Cf. A098550, A252865, A048793, A252868. Reading this sequence mod 2 gives A253050 and A253051. Cf. A253581, A253582, A253589 (binary weight), A253603. Analyzed further in A303596, A303597, A303598, A303599, A305368. The graphs of A109812, A252867, A305369, A305372 all have roughly the same, mysterious, fractal-like structure. - N. J. A. Sloane, Jun 03 2018 Sequence in context: A064365 A177356 A078322 * A194356 A227317 A224300 Adjacent sequences:  A252864 A252865 A252866 * A252868 A252869 A252870 KEYWORD nonn,base AUTHOR Franklin T. Adams-Watters, Dec 23 2014 STATUS approved

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Last modified October 22 15:11 EDT 2018. Contains 316490 sequences. (Running on oeis4.)