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A079051
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Recamán variation: a(0) = 0; for n >= 1, a(n) = a(n-1) - f(n) if that number is positive and not already in the sequence, otherwise a(n) = a(n-1) + f(n), where f(n) = floor(sqrt(n)) (A000196).
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7
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0, 1, 2, 3, 5, 7, 9, 11, 13, 10, 13, 16, 19, 22, 25, 28, 24, 20, 24, 28, 32, 36, 40, 44, 48, 43, 38, 33, 38, 43, 48, 53, 58, 63, 68, 73, 67, 61, 55, 49, 55, 61, 67, 73, 79, 85, 91, 97, 103, 96, 89, 82, 75, 82, 89, 96, 103, 110, 117, 124, 131, 138, 145, 152, 144, 136, 128, 120
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OFFSET
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0,3
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REFERENCES
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N. J. A. Sloane and Allan Wilks, On sequences of Recaman type, paper in preparation, 2006.
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LINKS
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FORMULA
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Conjecture: for n>100, 1/2 < a(n)/(n*log(n)) < 1.
The conjecture is false. In fact, a(n) = n^(3/2)/6 + O(n). - N. J. A. Sloane, Apr 29 2006
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MATHEMATICA
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Fold[Append[#1, If[MemberQ[#1, (a = #1[[-1]]) - (r = Floor@Sqrt@#2)], a + r, a - r]] &, {0, 1}, Range[2, 70]] (* Ivan Neretin, Apr 22 2018 *)
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PROG
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(PARI) lista(nn) = {va = vector(nn+1); last = 0; for (n=1, nn, new = last - sqrtint(n); if ((new <= 0) || vecsearch(vecsort(va, , 8), new), new = last + sqrtint(n)); va[n+1] = new; last = new; ); va; } \\ Michel Marcus, Apr 23 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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