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 A207901 Let S_k denote the first 2^k terms of this sequence and let b_k be the smallest positive integer that is not in S_k, also let R_k equal S_k read in reverse order; then the numbers b_k*R_k are the next 2^k terms. 17
 1, 2, 6, 3, 12, 24, 8, 4, 20, 40, 120, 60, 15, 30, 10, 5, 35, 70, 210, 105, 420, 840, 280, 140, 28, 56, 168, 84, 21, 42, 14, 7, 63, 126, 378, 189, 756, 1512, 504, 252, 1260, 2520, 7560, 3780, 945, 1890, 630, 315, 45, 90, 270, 135, 540, 1080, 360, 180, 36, 72, 216 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A permutation of the positive integers (but please note the starting offset: 0-indexed). This sequence is a variant of A052330. Shares with A064736, A302350, etc. the property that a(n) is either a divisor or a multiple of a(n+1). - Peter Munn, Apr 11 2018 on SeqFan-list. Note: A302781 is another such "divisor-or-multiple permutation" satisfying the same property. - Antti Karttunen, Apr 14 2018 The offset is 0 since S_0 = {1} denotes the first 2^0 = 1 terms. - Daniel Forgues, Apr 13 2018 This is "Fermi-Dirac piano played with Gray code", as indicated by Peter Munn's Apr 11 2018 formula. Compare also to A303771 and A302783. - Antti Karttunen, May 16 2018 LINKS Antti Karttunen, Table of n, a(n) for n = 0..8191 (first 1024 terms from Paul D. Hanna) Michel Marcus, Peter Munn, et al, Discussion on SeqFan-list FORMULA a(n) = A052330(A003188(n)). - Peter Munn, Apr 11 2018 a(n) = A302781(A302843(n)) = A302783(A064706(n)). - Antti Karttunen, Apr 16 2018 a(n+1) = A059897(a(n), A050376(A001511(n+1))). - Peter Munn, Apr 01 2019 EXAMPLE Start with ; appending 2* results in [1,2]; appending 3*[2,1] results in [1,2, 6,3]; appending 4*[3,6,2,1] results in [1,2,6,3, 12,24,8,4]; appending 5*[4,8,24,12,3,6,2,1] results in [1,2,6,3,12,24,8,4, 20,40,120,60,15,30,10,5]; next append 7*[5,10,30,15,60,120,40,20,4,8,24,12,3,6,2,1], multiplying by 7 since 6 is already found in the previous terms. Each new factor is in A050376: [2,3,4,5,7,9,11,13,16,17,19,23,25,29,...]. Continue in this way to generate all the terms of this sequence. MATHEMATICA a = {1}; Do[a = Join[a, Reverse[a]*Min[Complement[Range[Max[a] + 1], a]]], {n, 1, 6}]; a (* Ivan Neretin, May 09 2015 *) PROG (PARI) {A050376(n)= local(m, c, k, p); n--; if(n<=0, 2*(n==0), c=0; m=2; while( c0, if(n%2, p *= A050376(i)); i++; n >>= 1); (p); }; A003188(n) = bitxor(n, n>>1); A207901(n) = A052330(A003188(n)); \\ Antti Karttunen, Apr 13 2018 CROSSREFS Cf. A001511, A003188, A052330, A050376, A059897, A064706, A302029 (inverse), A302843. Cf. A064736, A281978, A282291, A302350, A302781, A302783, A303751, A303771, A304085, A304531, A304755 for other divisor-or-multiple permutations or conjectured permutations. Cf. A302033 (a squarefree analog), A304745. Sequence in context: A063929 A276158 A092393 * A054619 A054618 A120859 Adjacent sequences:  A207898 A207899 A207900 * A207902 A207903 A207904 KEYWORD nonn,look AUTHOR Paul D. Hanna, Feb 21 2012 EXTENSIONS Offset changed from 1 to 0 by Antti Karttunen, Apr 13 2018 STATUS approved

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Last modified December 3 00:59 EST 2021. Contains 349445 sequences. (Running on oeis4.)