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 A252868 Squarefree version of A252867. 4
 1, 2, 3, 10, 21, 5, 6, 35, 22, 15, 14, 33, 7, 30, 77, 26, 105, 13, 42, 65, 66, 91, 11, 70, 143, 210, 187, 39, 55, 78, 385, 34, 165, 182, 51, 110, 273, 85, 154, 195, 119, 330, 17, 231, 170, 429, 238, 715, 102, 455, 374, 1365, 38, 1155, 442, 57, 770, 663, 95, 462, 1105, 114, 1001, 255 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) = n if n <= 3, otherwise the first squarefree number not occurring earlier having at least one common factor with a(n-2), but none with a(n-1). The squarefree numbers are ordered by their occurrence in A019565. These represent the same sets of integers as A252867 does, but using the factorization of squarefree numbers for the representation. This is a permutation of the squarefree numbers. [I believe this is at present only a conjecture. - N. J. A. Sloane, Jan 10 2015] LINKS Chai Wah Wu, Table of n, a(n) for n = 1..10000 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. FORMULA a(n)=A019565(A252867(n-1)) MATHEMATICA (* b = A019565, c = A252867 *) b[n_] := Times @@ Prime[Flatten[Position[#, 1]]]&[Reverse[IntegerDigits[n, 2]]]; c[n_] := c[n] = If[n<3, n, For[k=3, True, k++, If[FreeQ[Array[c, n-1], k], If[BitAnd[k, c[n-2]] >= 1 && BitAnd[k, c[n-1]] == 0, Return[k]]]]]; a[n_] := b[c[n-1]]; Array[a, 64] (* Jean-François Alcover, Oct 03 2018 *) PROG (PARI) invecn(v, k, x)=for(i=1, k, if(v[i]==x, return(i))); 0 squarefree(n)=local(r=1, i=1); while(n>0, if(n%2, r*=prime(i)); i++; n\=2); r 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); vector(n, i, squarefree(v[i])) (Python) from operator import mul from functools import reduce from sympy import prime def A019565(n): ....return reduce(mul, (prime(i+1) for i, v in enumerate(bin(n)[:1:-1]) if v == '1')) if n > 0 else 1 A252868_list, l1, l2, s, b = [1, 2, 3], 2, 1, 3, set() for _ in range(10**4): ....i = s ....while True: ........if not (i in b or i & l1) and i & l2: ............A252868_list.append(A019565(i)) ............l2, l1 = l1, i ............b.add(i) ............while s in b: ................b.remove(s) ................s += 1 ............break ........i += 1 # Chai Wah Wu, Dec 25 2014 CROSSREFS Cf. A252867, A098550, A252865, A048793, A019565. Sequence in context: A226356 A141050 A252865 * A225477 A079161 A069565 Adjacent sequences:  A252865 A252866 A252867 * A252869 A252870 A252871 KEYWORD nonn AUTHOR Franklin T. Adams-Watters, Dec 23 2014 STATUS approved

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Last modified June 15 00:00 EDT 2021. Contains 345041 sequences. (Running on oeis4.)