A066220 Least k > 0 such that t^k = 1 mod (prime(n) - t) for 0 < t < prime(n).

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

Offset: 1

Author

Michael Ulm (taga(AT)hades.math.uni-rostock.de), Dec 18 2001

Keywords

• nonn

Comments

This sequence gives the period length of the base-p representation of HarmonicNumber[p-1]/p^2 (whose numerator is A061002).

Examples

			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 satisfies this.
		

Programs

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]]