A092028 a(n) is the smallest m > 1 such that m divides n^m-1.

2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 13, 2, 3, 2, 17, 2, 19, 2, 3, 2, 23, 2, 5, 2, 3, 2, 29, 2, 31, 2, 3, 2, 5, 2, 37, 2, 3, 2, 41, 2, 43, 2, 3, 2, 47, 2, 7, 2, 3, 2, 53, 2, 5, 2, 3, 2, 59, 2, 61, 2, 3, 2, 5, 2, 67, 2, 3, 2, 71, 2, 73, 2

Offset

3,1

Comments

Each prime factor of n-1 is a solution of the equation Mod[n^x-1,x]=0, so a(n) is not greater than smallest prime factor of n-1. Conjecture 1: All terms of this sequence are primes. Conjecture 2: a(n) is the smallest prime factor of n-1 or For n>2 A092028(n)=A020639(n-1).

Links

Charles R Greathouse IV, Table of n, a(n) for n = 3..10000

Formula

a[n_] := (For[k=2, Mod[n^k-1, k]>0, k++ ];k)

Example

a(8)=7 because 7 divides 8^7-1 and there doesn't exist an m such that 1<m<7 and m divides 8^m-1.

Mathematica

a[n_] := (For[k=2, Mod[n^k-1, k]>0, k++ ]; k); Table[a[n], {n, 3, 75}]

Prog

(PARI) a(n)=if(n%2, return(2)); my(m=3); while(Mod(n, m)^m!=1, m+=2); m \\ Charles R Greathouse IV, May 29 2014

Crossrefs

Cf. A020639, A092067.

Sequence in context: A086286 A272565 A135679 * A020639 A092067 A214606

Adjacent sequences: A092025 A092026 A092027 * A092029 A092030 A092031

Keyword

nonn

Author

Farideh Firoozbakht, Mar 26 2004

Status

approved