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A094761
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n + square excess of n.
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2
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0, 1, 3, 5, 4, 6, 8, 10, 12, 9, 11, 13, 15, 17, 19, 21, 16, 18, 20, 22, 24, 26, 28, 30, 32, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 64, 66, 68, 70, 72, 74, 76, 78
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| The trajectory of n under iteration of m -> a(m) is eventually constant iff n is a perfect square.
Conjecture (verified up to 727): the numbers not in this sequence are those of A008865. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 23 2009]
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REFERENCES
| S. H. Weintraub, An interesting recursion, Amer. Math. Monthly, 111 (No. 6, 2004), 528-530.
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LINKS
| S. H. Weintraub, An interesting recursion, Amer. Math. Monthly, 111 (No. 6, 2004), 528-530.
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FORMULA
| a(n) = n + A053186(n).
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MATHEMATICA
| f[n_] := 2 n - (Floor@ Sqrt@ n)^2; Table[f@ n, {n, 0, 71}] [From Robert G. Wilson, v (rgwv(AT)rgwv.com), Jan 23 2009]
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CROSSREFS
| Cf. A053186, A094763, A094764, A094765.
Sequence in context: A200324 A063259 A064425 * A114748 A182733 A107431
Adjacent sequences: A094758 A094759 A094760 * A094762 A094763 A094764
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jun 10 2004
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