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 A084693 a(n) is smallest positive integer not already in the sequence such that every partial sum is squarefree. 3
 1, 2, 3, 4, 5, 6, 8, 9, 13, 7, 11, 10, 12, 14, 17, 15, 18, 19, 16, 20, 21, 22, 24, 25, 27, 26, 28, 23, 29, 30, 32, 33, 31, 34, 36, 38, 37, 35, 40, 41, 39, 42, 43, 45, 46, 44, 48, 49, 51, 50, 47, 52, 55, 53, 56, 57, 54, 58, 59, 60, 61, 63, 64, 65, 62, 66, 67, 68, 69, 70, 72, 73 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Does every positive integer occur in the sequence? The longest string of consecutive numbers is 6. LINKS Michael De Vlieger, Table of n, a(n) for n = 0..1000 MATHEMATICA a = {1}; Do[k = 1; While[Nand[! MemberQ[a, k], SquareFreeQ[Sum[a[[i]], {i, n}] + k]], k++]; AppendTo[a, k], {n, 71}]; a (* Michael De Vlieger, Sep 03 2015 *) CROSSREFS Cf. A121644 (strictly increasing version). Sequence in context: A295165 A258023 A190232 * A276765 A121644 A259623 Adjacent sequences:  A084690 A084691 A084692 * A084694 A084695 A084696 KEYWORD nonn AUTHOR Amarnath Murthy, Jun 04 2003 EXTENSIONS More terms from David Wasserman, Dec 30 2004 STATUS approved

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Last modified December 4 09:35 EST 2020. Contains 338923 sequences. (Running on oeis4.)