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A293835
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a(n) = smallest number (in absolute value) not yet in the sequence such that the arithmetic mean of the first n terms a(1), a(2), ..., a(n) is an integer; a(1)=1. No two numbers with the same absolute value may appear. Preference is given to positive values of a(n).
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2
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1, 3, 2, 6, -7, -5, 0, 8, 10, 12, 14, 4, -9, -11, -13, -15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 16, -18, -20, -22, -24, -26, -28, -30, -32, -34, -36, -38, -40, -42, -44, -46, -48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78
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OFFSET
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1,2
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COMMENTS
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For n=1: 1/1 is an integer, and so is -1/1, but preference is given to positive values of a(n).
Fixed points so far: 1,8,17,50; i.e., aside from 1, these fixed points occur when sequence changes from 0 to positive or from negative to positive.
One could check the integers in order of appearance in A001057 to see if they are the next term. - David A. Corneth, Nov 13 2017
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LINKS
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EXAMPLE
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For n=7: (1 + 3 + 2 + 6 - 7 - 5 + 0)/7 is an integer.
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MATHEMATICA
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a[1] = 1; a[n_] := a[n] = For[k = 0, True, k++, aa = Array[a, n - 1]; If[FreeQ[aa, k | -k], If[IntegerQ[Mean[Append[aa, k]]], Return[k]]; If[IntegerQ[Mean[Append[aa, -k]]], Return[-k]]]];
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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