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A066220
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Least k > 0 such that t^k = 1 mod (prime(n) - t) for 0 < t < prime(n).
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0
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1, 1, 2, 4, 6, 60, 60, 120, 144, 7920, 55440, 18480, 7920, 27720, 2520, 637560, 8288280, 480720240, 480720240, 480720240, 480720240, 480720240, 1442160720, 9854764920, 59128589520, 59128589520, 147821473800, 670124014560
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| This sequence gives the period length of the base-p representation of HarmonicNumber[p-1]/p^2 (whose numerator is A061002).
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EXAMPLE
| a(5) = 6 because 2^6 = 1 mod 9, 3^6 = 1 mod 8, 4^6 = 1 mod 7, 5^6 = 1 mod 6, 6^6 = 1 mod 5, 7^6 = 1 mod 4, 8^6 = 1 mod 3, 9^6 = 1 mod 2 and 6 is the minimal exponent that verifies this.
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MATHEMATICA
| a[p_?PrimeQ] := Module[{e = 1}, While[! And @@ Table[Mod[PowerMod[i, e, p - i] - 1, p - i] == 0, {i, p - 1}], e++]; e]; a /@ Prime[Range[10]]
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CROSSREFS
| Sequence in context: A175877 A173818 A084324 * A009257 A098757 A056012
Adjacent sequences: A066217 A066218 A066219 * A066221 A066222 A066223
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KEYWORD
| nonn
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AUTHOR
| Michael Ulm (taga(AT)hades.math.uni-rostock.de), Dec 18 2001
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