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Search: id:A070194
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| A070194 |
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List the phi(n) numbers from 1 to n-1 which are relatively prime to n; sequence gives size of maximal gap. |
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+0
3
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| 1, 2, 1, 4, 1, 2, 2, 4, 1, 4, 1, 4, 3, 2, 1, 4, 1, 4, 3, 4, 1, 4, 2, 4, 2, 4, 1, 6, 1, 2, 3, 4, 3, 4, 1, 4, 3, 4, 1, 6, 1, 4, 3, 4, 1, 4, 2, 4, 3, 4, 1, 4, 3, 4, 3, 4, 1, 6, 1, 4, 3, 2, 3, 6, 1, 4, 3, 6, 1, 4, 1, 4, 3, 4, 3, 6, 1, 4, 2, 4, 1, 6, 3, 4, 3, 4, 1, 6, 3, 4, 3, 4, 3, 4, 1, 4, 3, 4, 1, 6, 1, 4, 5, 4, 1
(list; graph; listen)
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OFFSET
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3,2
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COMMENT
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Maximal gap in reduced residue system mod n.
It is an unsolved problem to determine the rate of growth of this sequence.
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REFERENCES
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H. L. Montgomery, Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis, Amer. Math. Soc., 1996, p. 200.
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LINKS
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T. D. Noe, Table of n, a(n) for n=3..10000
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EXAMPLE
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For n = 10 the reduced residues are 1, 3, 7, 9; the maximal gap is a(10) = 7-3 = 4.
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MATHEMATICA
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f[n_] := Block[{a = Select[ Table[i, {i, n - 1}], GCD[ #, n] == 1 & ], b = {}, k = 1, l = EulerPhi[n]}, While[k < l, b = Append[b, Abs[a[[k]] - a[[k + 1]]]]; k++ ]; Max[b]]; Table[ f[n], {n, 3, 100}]
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CROSSREFS
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Cf. A000010.
Sequence in context: A100762 A059147 A091891 this_sequence A105584 A072064 A105498
Adjacent sequences: A070191 A070192 A070193 this_sequence A070195 A070196 A070197
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), May 13 2002
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com) and John W. Layman (layman(AT)math.vt.edu), May 13 2002
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